Current fields of research

  • numerical treatment of PDEs
  • finite element method (FEM)
  • boundary element method (BEM)
  • a-posteriori error estimation and adaptive mesh-refinement strategies
  • cost-optimal interplay of mesh-refinement and iterative solvers
  • matrix compression and black-box preconditioning by use of hierarchical matrices
  • computational micromagnetics

Scientific publications

  1. M. Aldé, M. Feischl, D. Praetorius: BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics, part 1: Undconditional weak convergence to weak solutions, 2024
  2. A. Miraci, D. Praetorius, J. Streitberger: Unconditional full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs, [arXiv:2401.17778], 2024
  3. A. Bespalov, D. Praetorius, M. Ruggeri: Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals, arXiv:2208.09388, 2022

  1. A. Bespalov, D. Praetorius, T. Round, A. Savinov: Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM, SIAM/ASA Journal on Uncertainty Quantification, 13 (2025), 613-638  [www], [arXiv:2406.05028]
  2. M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs, Numerische Mathematik, 157 (2025), 409-445. [www] (open access), [arXiv:2401.06486]
  3. P. Bringmann, M. Brunner, D. Praetorius, J. Streitberger: Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs, Journal of Numerical Mathematics, published online first (2024). [www] (open access), [arXiv:2312.00489]
  4. P. Bringmann, M. Feischl, A. Miraci, D. Praetorius, J. Streitberger:On full linear convergence and optimal complexity of adaptive FEM with inexact solver, Computers & Mathematics with Applications, 180 (2025), 102-129. [www] (open access), [arXiv:2311.15738]
  5. P. Bringmann, A. Miraci, D. Praetorius: Iterative solvers in adaptive FEM, Advances in Applied Mechanics, 59 (2024), 147-212. [www], arXiv:2404.07126
  6. M. Brunner, P. Heid, M. Innerberger, A. Miraci, D. Praetorius, J. Streitberger: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs, IMA Journal of Numerical Analysis, 44 (2024), 1560–1596 and 1903–1909. [www] (open access), [corrigendum] (open access), [arXiv:2212.00353]
  7. M. Innerberger, A. Miraci, D. Praetorius, J. Streitberger: hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2024), 247–272. [www] (open access), arXiv:2210.10415]
  8. R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D.Praetorius: Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, 57 (2023), 2193–2225. [www] (open access), [arXiv:2211.04123]
  9. R. Becker, G. Gantner, M. Innerberger, D.Praetorius: Goal-oriented adaptive finite element methods with optimal computational complexity, Numerische Mathematik, 153 (2023), 111–140. [www] (open access), [arXiv:2101.11407]
  10. G. Di Fratta, A. Jüngel, D. Praetorius, V. Slastikov: Spin-diffusion model for micromagnetics in the limit of long times, Journal of Differential Equations, 343 (2023), 467–494. [www], [arXiv:2009.14534]
  11. G. Di Fratta, C.-M. Pfeiler, D. Praetorius, M. Ruggeri: The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics, Computational Methods in Applied Mathematics, 23 (2023), 145–175. [www] (open access), [arXiv:2203.06445]
  12. V. Helml, M. Innerberger, D. Praetorius: Plain convergence of goal-oriented adaptive FEM, Computers & Mathematics with Applications, 147 (2023), 130–149. [www] (open access), [arXiv:2208.10143]
  13. M. Innerberger, D. Praetorius: MooAFEM: An object oriented Matlab code for higher-order (nonlinear) adaptive FEM, Applied Mathematics and Computation, 442 (2023), #127731 (17 pages). [www] (open access), [arXiv:2203.01845]
  14. A.A.S. Amad, P.D. Ledger, T. Betcke, D. Praetorius: Benchmark computations for the polarization tensor characterization of small conducting objects, Applied Mathematical Modelling, 111 (2022), 94–107. [www] (open access), [arXiv:2106.15157]
  15. R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D.Praetorius: Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs, Computers & Mathematics with Applications, 118 (2022), 18–35. [www] (open access), [arXiv:2112.06687]
  16. R. Becker, M. Innerberger, D. Praetorius: Adaptive FEM for parameter-errors in elliptic linearquadratic parameter estimation problems, SIAM Journal on Numerical Analysis, 60 (2022), 1450– 1471. [www], [arXiv:2111.03627]
  17. A. Bespalov, D. Praetorius, M. Ruggeri: Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM, IMA Journal of Numerical Analysis, 42 (2022), 2190–2213. [www]
  18. A. Buffa, G. Gantner, C. Gianelli, D. Praetorius, R. Vazquez: Mathematical foundations of adaptive isogeometric analysis, Archives of Computational Methods in Engineering, 29 (2022), 4479–4555. [www] (open access), [arXiv:2107.02023]
  19. E. Davoli, G. Di Fratta, D. Praetorius, M. Ruggeri: Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction, Mathematical Models and Methods in Applied Sciences (M3AS), 32 (2022), 911–939. [www], [arXiv:2010.15541]
  20. G. Gantner, D. Praetorius: Plain convergence of adaptive algorithms without exploiting reliability and efficiency, IMA Journal of Numerical Analysis, 42 (2022), 1434–1453. [www] (open access), [arXiv:2009.01349]
  21. G. Gantner, D. Praetorius: Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations, Applicable Analysis, 101 (2022), 2085–2118. [www] (open access), [arXiv:2004.07762]
  22. G. Gantner, D. Praetorius: Adaptive BEM for elliptic PDE systems, Part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations, Computers & Mathematics with Applications, 117 (2022), 74–76. [www] (open access), [arXiv:2107.06613]
  23. G. Gantner, D. Praetorius, S. Schimanko: Stable implementation of adaptive IGABEM in 2D in Matlab, Computational Methods in Applied Mathematics, 22 (2022), 563–590. [www] (open access), [arXiv:2203.01845]
  24. A. Kovacs, L. Exl, A. Kornell, J. Fischbacher, M. Hovorka, M. Gusenbauer, L. Breth, H. Oezelt, D. Praetorius, D. Suess, T. Schrefl: Magnetostatics and micromagnetics with physics informed neural networks, Journal of Magnetism and Magnetic Materials, 548 (2022), #168591 (12 pages). [www] (open access), [arXiv:2106.03362]
  25. N.J. Mauser, C.-M. Pfeiler, D. Praetorius, M. Ruggeri: Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics, Applied Numerical Mathematics, 180 (2022), 33–54. [www] (open access), [arXiv:2112.00451]
  26. H. Oezelt, L. Qu, A. Kovacs, J. Fischbacher, M. Gusenbauer, R. Beigelbeck, D. Praetorius, Y. Masao, T. Shoji, A. Kato, R. Chantrell, M. Winklhofer, G. Zimanyi, T. Schrefl: Full-spin-wave-scaled stochastic micromagnetism for mesh-independent simulations of ferromagnetic resonance and reversal, npj Computational Materials, 8 (2022), #35 (9 pages). [www] (open access)
  27. R. Becker, M. Innerberger, D. Praetorius: Optimal convergence rates for goal-oriented FEM with quadratic goal functional, Computational Methods in Applied Mathematics, 21 (2021), 267–288. [www] (open access), [arXiv:2003.13270]
  28. A. Bespalov, D. Praetorius, M. Ruggeri: Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM, SIAM/ASA Journal on Uncertainty Quantification, 90 (2021), 1184– 1216. [www], [arXiv:2006.02255]
  29. M. Faustmann, J. Melenk, D. Praetorius: Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian, Mathematics of Computation, 90 (2021), 1557–1587. [www]
  30. G. Gantner, A. Haberl, D. Praetorius, S. Schimanko: Rate optimality of adaptive finite element methods with respect to overall computational costs, Mathematics of Computation, 90 (2021), 2011–2040. [www], [arXiv:2003.10785]
  31. A. Haberl, D. Praetorius, S. Schimanko, M. Vohralik: Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver, Numerische Mathematik, 147 (2021), 679–725. [www] (open access), [arXiv:2004.13137]
  32. P. Heid, D. Praetorius, T. Wihler: Energy contraction and optimal convergence of adaptive iterative linearized finite element methods, Computational Methods in Applied Mathematics, 21 (2021), 407–422. [www], [arXiv:2007.10750]
  33. M. Innerberger, D. Praetorius: Instance-optimal goal-oriented adaptivity, Computational Methods in Applied Mathematics, 21 (2021), 109–126. [www] [arXiv:1907.13035]
  34. S. Kurz, D. Pauly, D. Praetorius, S. Repin, D. Sebastian: Functional a posteriori error estimates for boundary element methods, Numerische Mathematik, 147 (2021), 937–966. [www] (open access), [arXiv:1912.05789]
  35. D. Praetorius, S. Repin, S. Sauter: Reliable Methods of Mathematical Modeling (Editorial of Special Issue of RMMM 2019 Conference), Computational Methods in Applied Mathematics, 21 (2021), 263–266. [www] (open access)
  36. G. Di Fratta, M. Innerberger, D. Praetorius: Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics, Nonlinear Analysis: Real-World Applications, 55 (2020), #103122 (13 pages). [www], [arXiv:1910.04630]
  37. G. Di Fratta, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, B. Stiftner: Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation, IMA Journal of Numerical Analysis, 40 (2020), 2802–2838. [www], [arXiv:1711.10715]
  38. C. Erath, G. Gantner, D. Praetorius: Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators, Computers & Mathematics with Applications, 79 (2020), 623– 642. [www] (open access), [arXiv:1805.00715]
  39. T. Führer, D. Praetorius: A short note on plain convergence of adaptive least-squares finite element methods, Computers & Mathematics with Applications, 80 (2020), 1619–1632. [www] (open access), [arXiv:2005.11015]
  40. G. Gantner, D. Praetorius: Adaptive IGAFEM with optimal convergence rates: T-splines, Computer Aided Geometric Design, 81 (2020), #101906 (20 pages). [www] (open access), [arXiv:1910.01311]
  41. G. Gantner, D. Praetorius, S. Schimanko: Adaptive isogeometric boundary element methods with local smoothness control, Mathematical Models and Methods in Applied Sciences (M3AS), 30 (2020), 261–307. [www], [arXiv:1903.01830]
  42. C.-M. Pfeiler, M. Ruggeri, B. Stiftner, L. Exl, M. Hochsteger, G. Hrkac, J. Schöberl, N. Mauser, D. Praetorius: Computational micromagnetics with Commics, Computer Physics Communications, 248 (2020), #106965 (11 pages). [www], [arXiv:1812.05931]
  43. C.-M. Pfeiler, D. Praetorius: Dörfler marking with minimal cardinality is a linear complexity problem, Mathematics of Computation, 89 (2020), 2735–2752. [www], [arXiv:1907.13078]
  44. D. Praetorius, M. Ruggeri, E. Stephan: The saturation assumption yields optimal convergence of two-level adaptive BEM, Applied Numerical Mathematics, 152 (2020), 105–124. [www], [arXiv:1907.06612]
  45. A. Bespalov, T. Betcke, A. Haberl, D. Praetorius: Adaptive BEM with optimal convergence rates for the Helmholtz equation, Computer Methods in Applied Mechanics and Engineering, 346 (2019), 260–287. [www], [arXiv:1807.11802]
  46. A. Bespalov, D. Praetorius, L. Rocchi, M. Ruggeri: Convergence of adaptive stochastic Galerkin FEM, SIAM Journal on Numerical Analysis, 57 (2019), 2359–2382. [www], [arXiv:1811.09462]
  47. A. Bespalov, D. Praetorius, L. Rocchi, M. Ruggeri: Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs, Computer Methods in Applied Mechanics and Engineering, 345 (2019), 951–982. [www], [arXiv:1806.03928]
  48. T. Betcke, A. Haberl, D. Praetorius: Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra, Journal of Computational Physics, 397 (2019), #108837 (19 pages) [www], [arXiv:1901.08393]
  49. G. Di Fratta, T. Führer, G. Gantner, D. Praetorius: Adaptive Uzawa algorithm for the Stokes equation, M2AN Mathematical Modelling and Numerical Analysis, 53 (2019), 1841–1870. [www], [arXiv:1812.11798]
  50. C. Erath, D. Praetorius: Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs, IMA Journal of Numerical Analysis, 39 (2019), 983–1008. [www], [arXiv:1709.07181]
  51. C. Erath, D. Praetorius: Optimal adaptivity for the SUPG finite element method, Computer Methods in Applied Mechanics and Engineering, 353 (2019), 308–327. [www], [arXiv:1806.11000]
  52. T. Führer, G. Gantner, D. Praetorius, S. Schimanko: Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods, Computer Methods in Applied Mechanics and Engineering, 351 (2019), 571–598. [www], [arXiv:1808.04585]
  53. T. Führer, A. Haberl, D. Praetorius, S. Schimanko: Adaptive BEM with inexact PCG solver yields almost optimal computational costs, Numerische Mathematik, 141 (2019), 967–1008. [www] (open access), [arXiv:1806.00313]
  54. G. Hrkac, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, A. Segatti, B. Stiftner: Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics, Advances in Computational Mathematics, 45 (2019), 1329–1368. [www], [arXiv:1712.03795]
  55. J. Kraus, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, B. Stiftner: Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics, Journal of Computational Physics, 398 (2019), #108866 (27 pages). [www], [arXiv:1808.10281]
  56. T. Führer, D. Praetorius: A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems, Computers & Mathematics with Applications, 75 (2018), 2678–2697. [www], [arXiv:1703.10796]
  57. G. Gantner, A. Haberl, D. Praetorius, B. Stiftner: Rate optimal adaptive FEM with inexact solver for nonlinear operators, IMA Journal of Numerical Analysis, 38 (2018), 2678–2697. [www], [arXiv:1611.05212]
  58. D. Praetorius, M. Ruggeri, B. Stiftner: Convergence of an implicit-explicit midpoint scheme for computational micromagnetics, Computers & Mathematics with Applications, 75 (2018), 1719– 1738. [www], [arXiv:1611.02465]
  59. M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Local inverse estimates for non-local boundary integral operators, Mathematics of Computation, 86 (2017), 2651–2686. [www], [arXiv:1504.04394]
  60. A. Bespalov, A. Haberl, D. Praetorius: Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems, Computer Methods in Applied Mechanics and Engineering, 317 (2017), 318–340. [www], [arXiv:1606.08319]
  61. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator, IMA Journal of Numerical Analysis, 37 (2017), 1211–1244. [www], [arXiv:1503.01943]
  62. M. Feischl, T. Führer, D. Praetorius, E. Stephan: Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations, Calcolo, 54 (2017), 367–399. [www]
  63. M. Feischl, T. Führer, D. Praetorius, E. Stephan: Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements, Numerical Methods for Partial Differential Equations, 33 (2017), 603–632. [www], [arXiv:1311.5782]
  64. M. Feischl, G. Gantner, A. Haberl, D. Praetorius: Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations, Numerische Mathematik, 136 (2017), 147–182. [www], [arXiv:1510.05111]
  65. G. Gantner, D. Haberlik, D. Praetorius: Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines, M3AS Mathematical Models and Methods in Applied Sciences, 27 (2017), 2631–2674. [www], [arXiv:1701.07764]
  66. J.M. Melenk, D. Praetorius, B. Wohlmuth: Simultaneous quasi-optimal convergence rates in FEMBEM coupling, M2AS Mathematical Methods in the Applied Sciences, 40 (2017), 463–485. [www], [arXiv:1404.2744]
  67. C. Abert, M. Ruggeri, F. Bruckner, C. Vogler, A. Manchon, D. Praetorius, D. Süss: A self-consistent spin-diffusion model for micromagnetics, Scientific Reports, 6 (2016), 16. [www]
  68. C. Erath, D. Praetorius: Adaptive finite volume methods with convergence rates, SIAM Journal on Numerical Analysis, 54 (2016), 2228–2255. [www], [arXiv:1508.06155]
  69. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H -matrix approximants to the inverses of BEM matrices: the simple-layer operator, Mathematics of Computation, 85 (2016), 119–152. [www], [arXiv:1311.5028]
  70. M. Feischl, T. Führer, G. Gantner, A. Haberl, D. Praetorius: Adaptive boundary element methods for optimal convergence of point errors, Numerische Mathematik, 132 (2016), 541–567. [www]
  71. M. Feischl, T. Führer, M. Niederer, S. Strommer, A. Steinböck, D. Praetorius: Efficient numerical computation of direct exchange areas in thermal radiation analysis, Numerical Heat Transfer, Part B: Fundamentals, 69 (2016), 511–533. [www]
  72. M. Feischl, G. Gantner, A. Haberl, D. Praetorius: Adaptive 2D IGA boundary element methods, Engineering Analysis with Boundary Elements, 62 (2016), 141–153. [www], [arXiv:1504.06164]
  73. M. Feischl, D. Praetorius, K. van der Zee: An abstract analysis of optimal goal-oriented adaptivity, SIAM Journal on Numerical Analysis, 54 (2016), 1423–1448. [www], [arXiv:1505.04536]
  74. M. Ruggeri, C. Abert, G. Hrkac, D. Süss, D. Praetorius: Coupling of dynamical micromagnetism and a stationary spin drift-diffusion equation: A step towards a fully self-consistent spintronics framework, Physica B: Condensed Matter, 486 (2016), 88–91. [www]
  75. C. Vogler, C. Abert, F. Bruckner, D. Süss, D. Praetorius: Heat-assisted magnetic recording of bitpatterned media beyond 10 Tb/in2, Applied Physics Letters, 108 (2016), 102406-1-102406-4. [www]
  76. C. Vogler, C. Abert, F. Bruckner, D. Süss, D. Praetorius: Areal density optimization for heat-assisted magnetic recording on high-density media, Journal of Applied Physics, 119 (2016), 223903. [www]
  77. C. Vogler, C. Abert, F. Bruckner, D. Süss, D. Praetorius: Influence of grain size and exchange interaction on the LLB modeling procedure, Journal of Applied Physics, 120 (2016), 223903. [www]
  78. C. Vogler, C. Abert, F. Bruckner, D. Süss, D. Praetorius: Basic noise mechanisms of heat-assisted magnetic recording, 120 (2016), 153901. [www]
  79. C. Abert, M. Ruggeri, F. Bruckner, C. Vogler, G. Hrkac, D. Praetorius, D. Süss: A three-dimensional spin-diffusion model for micromagnetics, Scientific Reports, 5 (2015), 14855. [www]
  80. M. Aurada, M. Feischl, T. Führer, M. Karkulik, D. Praetorius: Energy norm based error estimators for adaptive BEM for hypersingular integral equations, Applied Numerical Mathematics, 95 (2015), 15–35. [www]
  81. M. Aurada, J.M. Melenk, D. Praetorius: FEM-BEM Coupling for the large-body limit in micromagnetics, Journal of Computational and Applied Mathematics, 281 (2015), 10–31. [www]
  82. L. Banas, M. Page, D. Praetorius: A convergent linear finite element scheme for the MaxwellLandau-Lifshitz-Gilbert equations, ETNA Electronic Transactions on Numerical Analysis, 44 (2015), 250–270. [www], [arXiv:1303.4009]
  83. M. Faustmann, J.M. Melenk, D. Praetorius: H-matrix approximability of the inverses of FEM matrices, Numerische Mathematik, 131 (2015), 615–642. [www], [arXiv:1308.0499]
  84. M. Feischl, T. Führer, N. Heuer, M. Karkulik, D. Praetorius: Adaptive boundary element methods: A posteriori error estimators, adaptivity, convergence, and implementation, Archives of Computational Methods in Engineering, 22 (2015), 309–389. [www] [arXiv:1402.0744]
  85. M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Quasi-optimal convergence rates for adaptive boundary element methods with data approximation - Part II: Hyper-singular integral equation, ETNA Electronic Transactions on Numerical Analysis, 44 (2015), 153–176. [www]
  86. M. Feischl, T. Führer, M. Karkulik, D. Praetorius: Stability of symmetric and nonsymmetric FEMBEM couplings for nonlinear elasticity problems, Numerische Mathematik, 130 (2015), 199–223. [www], [arXiv:1212.2620]
  87. M. Feischl, G. Gantner, D. Praetorius: Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations, Computer Methods in Applied Mechanics and Engineering, 290 (2015), 362–386. [www], [arXiv:1408.2693]
  88. T. Führer, J.M. Melenk, D. Praetorius, A. Rieder: Optimal additive Schwarz methods for the hpBEM: the hypersingular integral operator in 3D on locally refined meshes, Computers & Mathematics with Applications, 70 (2015), 1583–1605. [www], [arXiv:1412.2024]
  89. K. Le, M. Page, D. Praetorius, T. Tran: On a decoupled linear FEM integrator for eddy-current-LLG, Applicable Analysis, 84 (2015), 1051–1067. [www], [arXiv:1306.3319]
  90. C. Abert, G. Hrkac, M. Page, D. Praetorius, M. Ruggeri, D. Süss: Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator, Computers & Mathematics with Applications, 68 (2014), 639–654. [www], [arXiv:1402.0983]
  91. M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius: HILBERT - A MATLAB implementation of adaptive 2D-BEM, Numerical Algorithms, 67 (2014), 1–32. [www]
  92. M. Aurada, J.M. Melenk, D. Praetorius: Mixed conforming elements for the large-body limit in micromagnetics, M3AS Mathematical Models and Methods in Applied Sciences, 24 (2014), 113– 144. [www]
  93. L. Banas, M. Page, D. Praetorius, J. Rochat: A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction, IMA Journal of Numerical Analysis, 34 (2014), 1361–1385. [www], [arXiv:1303.4060]
  94. F. Bruckner, M. Feischl, T. Führer, P. Goldenits, M. Page, D. Praetorius, M. Ruggeri, D. Süss: Multiscale modeling in micromagnetics: Existence of solutions and numerical integration, M3AS Mathematical Models and Methods in Applied Sciences, 24 (2014), 2627–2662. [www], [arXiv:1209.5548]
  95. C. Carstensen, M. Feischl, M. Page, D. Praetorius: Axioms of adaptivity, Computers & Mathematics with Applications, 67 (2014), 1195–1253. [www], [arXiv:1312.1171]
  96. M. Faustmann, J.M. Melenk, D. Praetorius: A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian, Springer Lecture Notes in Computational Science and Engineering, 95 (2014), 249–259. [www]
  97. M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: Weakly-singular integral equation, Calcolo, 51 (2014), 531–562. [www]
  98. M. Feischl, T. Führer, G. Mitscha-Eibl, D. Praetorius, E. Stephan: Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor, Computational Methods in Applied Mathematics, 14 (2014), 485–508. [www], [arXiv:1405.5306]
  99. M. Feischl, T. Führer, M. Karkulik, D. Praetorius: ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve, Engineering Analysis with Boundary Elements, 38 (2014), 49–60. [www] [arXiv:1306.5120]
  100. M. Feischl, T. Führer, D. Praetorius: Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems, SIAM Journal on Numerical Analysis, 52 (2014), 601–625. [www], [arXiv:1210.8369]
  101. M. Feischl, M. Page, D. Praetorius: Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data, International Journal of Numerical Analysis & Modeling, 11 (2014), 229–253. [www], [arXiv:1207.3257]
  102. M. Feischl, M. Page, D. Praetorius: Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data, Journal of Computational and Applied Mathematics, 255 (2014), 481– 501. [www], [arXiv:1306.5100]
  103. M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity, Computational Mechanics, 51 (2013), 399–419. [www], [arXiv:1211.4225]
  104. M. Aurada, M. Feischl, T. Führer, M. Karkulik, D. Praetorius: Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods, Computational Methods in Applied Mathematics, 13 (2013), 305–332. [www]
  105. M. Aurada, M. Feischl, J. Kemetmüller, M. Page, D. Praetorius: Each H1/2-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd, M2AN Mathematical Modelling and Numerical Analysis, 47 (2013), 1207–1235. [www], [arXiv:1306.5115]
  106. F. Bruckner, C. Vogler, B. Bergmair, T. Huber, M. Fuger, D. Süss, M. Feischl, T. Führer, M. Page, D. Praetorius: Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations, Journal of Magnetism and Magnetic Materials, 343 (2013), 163–168. [www]
  107. C. Erath, S. Funken, P. Goldenits, D. Praetorius: Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D, Applicable Analysis, 92 (2013), 1194-1216. [www]
  108. M. Feischl, M. Karkulik, J.M. Melenk, D. Praetorius: Quasi-optimal convergence rate for an adaptive boundary element method, SIAM Journal on Numerical Analysis, 51 (2013), 1327–1348. [www]
  109. M. Karkulik, G. Of, D. Praetorius: Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement, Numerical Methods for Partial Differential Equations, 29 (2013), 2081–2106. [www]
  110. M. Karkulik, D. Pavlicek, D. Praetorius: On 2D newest vertex bisection: Optimality of mesh-closure and H1-stability of L2-projection, Constructive Approximation, 38 (2013), 213–234. [www], [arXiv:1210.0367]
  111. M. Page, D. Praetorius: Convergence of adaptive FEM for some elliptic obstacle problem, Applicable Analysis, 92 (2013), 595–615. [www]
  112. M. Aurada, M. Feischl, M. Karkulik, D. Praetorius: A posteriori error estimates for the JohnsonNédélec FEM-BEM coupling, Engineering Analysis with Boundary Elements, 36 (2012), 255–266. [www]
  113. M. Aurada, M. Feischl, D. Praetorius: Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems, M2AN Mathematical Modelling and Numerical Analysis, 46 (2012), 1147–1173. [www]
  114. M. Aurada, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius: Convergence of adaptive BEM for some mixed boundary value problem, Applied Numerical Mathematics, 62 (2012), 226–245. [www]
  115. M. Aurada, S. Ferraz-Leite, D. Praetorius: Estimator reduction and convergence of adaptive BEM, Applied Numerical Mathematics, 62 (2012), 787–801. [www]
  116. F. Bruckner, C. Vogler, M. Feischl, D. Praetorius, B. Bergmair, T. Huber, M. Fuger, D. Süss: 3D FEM-BEM-coupling method to solve magnetostatic Maxwell equations, Journal of Magnetism and Magnetic Materials, 324 (2012), 1862–1866. [www]
  117. C. Carstensen, D. Praetorius: Stabilization yields strong convergence of macroscopic magnetization vectors for micromagnetics without exchange energy, Journal of Numerical Mathematics, 20 (2012), 81–109. [www]
  118. C. Carstensen, D. Praetorius: Convergence of adaptive boundary element methods, Journal of Integral Equations and Applications, 24 (2012), 1–23. [www]
  119. S. Ferraz-Leite, J.M. Melenk, D. Praetorius: Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics, Numerische Mathematik, 122 (2012), 101–131. [www]
  120. S. Funken, D. Praetorius, P. Wissgott: Efficient implementation of adaptive P1-FEM in MATLAB, Computational Methods in Applied Mathematics, 11 (2011), 460–490. [www]
  121. C. Ortner, D. Praetorius: On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems, SIAM Journal on Numerical Analysis, 49 (2011), 346–367. [www]
  122. S. Ferraz-Leite, C. Ortner, D. Praetorius: Convergence of simple adaptive Galerkin schemes based on h−h/2 error estimators, Numerische Mathematik, 116 (2010), 291–316. [www]
  123. O. Koch, R. März, D. Praetorius, E. Weinmüller: Collocation methods for index 1 DAEs with a singularity of the first kind, Mathematics of Computation, 79 (2010), 281–304. [www]
  124. C. Erath, S. Ferraz-Leite, S. Funken, D. Praetorius: Energy norm based a posteriori error estimation for boundary element methods in two dimensions, Applied Numerical Mathematics, 59 (2009), 2713–2734. [www]
  125. C. Erath, D. Praetorius: A posteriori error estimate and adaptive mesh-refinement for the cell-centered finite volume method for elliptic boundary value problems, SIAM Journal on Numerical Analysis, 47 (2008), 109–135. [www]
  126. S. Ferraz-Leite, D. Praetorius: Simple a posteriori error estimators for the h-version of the boundary element method, Computing, 83 (2008), 135–162. [www]
  127. C. Carstensen, D. Praetorius: Averaging techniques for a posteriori error control in finite element and boundary element analysis, Lecture Notes in Applied and Computational Mechanics, 29 (2007), 29–59. [www]
  128. C. Carstensen, D. Praetorius: On stabilized models in micromagnetics, Computational Mechanics, 39 (2007), 663–672. [www]
  129. C. Carstensen, D. Praetorius: Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions, SIAM Journal on Scientific Computing, 29 (2007), 782–810. [www]
  130. N. Popovic, D. Praetorius, A. Schlömerkemper: Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Part I: Analysis, Continuum Mechanics and Thermodynamics, 19 (2007), 67–80. [www]
  131. N. Popovic, D. Praetorius, A. Schlömerkemper: Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Part II: Numerical simulation, Continuum Mechanics and Thermodynamics, 19 (2007), 81–109. [www]
  132. C. Carstensen, D. Praetorius: Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind, SIAM Journal on Scientific Computing, 27 (2006), 1226–1260. [www]
  133. N. Popovic, D. Praetorius: H-matrix techniques for stray-field computations in computational micromagnetics, Lecture Notes in Computer Science, 3743 (2006), 102–110. [www]
  134. W. Auzinger, O. Koch, D. Praetorius, E. Weinmüller: New a-posteriori error estimates for singular boundary value problems, Numerical Algorithms, 40 (2005), 79–100. [www]
  135. C. Carstensen, D. Praetorius: Numerical analysis for a macroscopic model in micromagnetics, SIAM Journal on Numerical Analysis, 42 (2005), 2633–2651. [www]
  136. C. Carstensen, D. Praetorius: Effective simulation of a macroscopic model for stationary micromagnetics, Computer Methods in Applied Mechanics and Engineering, 194 (2005), 531–548. [www]
  137. N. Popovic, D. Praetorius: Applications of H-matrix techniques in micromagnetics, Computing, 74 (2005), 177–204. [www]
  138. C. Carstensen, M. Maischak, E. Stephan, D. Praetorius: Residual-based a posteriori error estimate for hypersingular equation on surfaces, Numerische Mathematik, 97 (2004), 397–426. [www]
  139. C. Carstensen, D. Praetorius: A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind, SIAM Journal on Scientific Computing, 25 (2004), 259–283. [www]
  140. D. Praetorius: Analysis of the operator ∆−1div arising in magnetic models, Zeitschrift für Analysis und ihre Anwendungen, 23 (2004), 589–605. [www]
  141. D. Praetorius: Remarks and examples concerning distance ellipsoids, Colloquium Mathematicum, 93 (2002), 41–53. [www]

  1. M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM for semilinear elliptic PDEs, Proceedings of ENUMATH 2023, Volume 1, Lecture Notes in Computational Science and Engineering, 153, 209–219, 2025. [www], [preprint]
  2. M. Brunner, D. Praetorius, J. Streitberger: Optimal cost of (goal-oriented) adaptive FEM for general second-order linear elliptic PDEs, Volume 1, Proceedings of ENUMATH 2023, Lecture Notes in Computational Science and Engineering, 153, 2025. [www], [preprint]
  3. C. Erath, D. Praetorius: Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM, in: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects (FVCA 2017), Springer, Wien, 2017, pp. 215–223. [www]
  4. P. Goldenits, G. Hrkac, D. Praetorius, D. Süss: An effective integrator for the Landau-Lifshitz-Gilbert equation, MATHMOD 2012 – 7th Vienna Conference on Mathematical Modelling, International Federation of Automatic Control, Mathematical Modelling, Volume 7, Part 1 (2012), pp. 493–497. [www]
  5. M. Aurada, M. Feischl, M. Karkulik, D. Praetorius: Adaptive coupling of FEM and BEM: Simple error estimators and convergence, Proceedings in Applied Mathematics and Mechanics (PAMM), 11 (2011), 755–756. [www]
  6. M. Feischl, M. Page, D. Praetorius: Convergence of adaptive FEM for elliptic obstacle problems, Proceedings in Applied Mathematics and Mechanics (PAMM), 11 (2011), 767–768. [www]
  7. M. Feischl, M. Page, D. Praetorius: Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data, Proceedings in Applied Mathematics and Mechanics (PAMM), 11 (2011), 769–772. [www]
  8. P. Goldenits, D. Praetorius, D. Süss: Convergent geometric integrator for the Landau-Lifshitz Gilbert equation in micromagnetics, Proceedings in Applied Mathematics and Mechanics (PAMM), 11 (2011), 775–776. [www]
  9. M. Aurada, J.M. Melenk, D. Praetorius: Mixed conforming elements for the large-body limit in micromagnetics, Proceedings of MATHMOD 09 – 6th Vienna Conference on Mathematical Modelling, ARGESIM Report no. 35 (2009), 2296–2303. [www]
  10. S. Ferraz-Leite, J.M. Melenk, D. Praetorius: Reduced model in thin-film micromagnetics, Proceedings of MATHMOD 09 – 6th Vienna Conference on Mathematical Modelling, ARGESIM Report no. 35 (2009), 2287–2295. [www]
  11. C. Erath, S. Funken, D. Praetorius: Adaptive cell-centered finite volume method, in: Finite Volumes for Complex Applications V, R. Eymard, J. Hérard (eds.), John Wiley & Sons, (2008), pp. 359-366.
  12. W. Boiger, C. Carstensen, D. Praetorius: Strong convergence for large bodies in micromagnetics, Proceedings in Applied Mathematics and Mechanics (PAMM), 7 (2007), 1151203–1151204. [www]
  13. N. Popovic, D. Praetorius, A. Schlömerkemper: Magnetic force formulae for magnets at small distances, Proceedings in Applied Mathematics and Mechanics (PAMM), 5 (2005), 631–632. [www]
  14. C. Carstensen, D. Praetorius: On stabilized models in micromagnetics, Proceedings of ECCOMAS 2004 – 4th European Congress on Computational Methods in Applied Sciences and Engineering, Proceedings Volume II, (2004).

  1. S. Kurz, D. Pauly, D. Praetorius, S. Repin, D. Sebastian: Functional a-posteriori error estimates for BEM, Oberwolfach Workshop on Boundary Element Methods, Oberwolfach Reports, European Mathematical Society, 17/2020 (2020).
  2. G. Gantner, A. Haberl, D. Praetorius, B. Stiftner: Rate optimal adaptive FEM with inexact solver for strongly monotone operators, Oberwolfach Workshop on Adaptive Algorithms, Oberwolfach Reports, European Mathematical Society, 44/2016 (2016).
  3. M. Ruggeri, D. Praetorius, B. Stiftner: Coupling and numerical integration of the Landau-LifshitzGilbert equation, Oberwolfach Workshop on Mathematics of Magnetoelastic Materials, Oberwolfach Reports, European Mathematical Society, 51/2016 (2016).
  4. C. Carstensen, M. Feischl, D. Praetorius: Rate optimality of adaptive algorithms, ECCOMAS Newsletter, 07 (2014), 20–23.
  5. C. Carstensen, M. Feischl, D. Praetorius: Rate optimality of adaptive algorithms: An axiomatic approach, part II: Extensions, Proceedings of 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, 2014, pp. 2511–2522.
  6. M. Feischl, T. Führer, D. Praetorius, E. Stephan: Optimal preconditioning for the coupling of adaptive finite elements and boundary elements, Proceedings of 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, 2014, pp. 2108–2119.
  7. M. Feischl, G. Gantner, D. Praetorius: A posteriori error estimation for adaptive IGA boundary element methods, Proceedings of 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, 2014, pp. 2421–2432.
  8. M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Novel inverse estimates for non-local operators, Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, pp. 79–84.
  9. M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: FEM-BEM couplings without stabilization, Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, pp. 48–53.
  10. M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius: Quasi-optimal adaptive BEM, Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, pp. 44–47.
  11. F. Reichel, T. Schrefl, D. Süss, G. Hrkac, D. Praetorius, M. Gusenbauer, S. Bance, H. Oezelt, J. Fischbacher, L. Exl: Mechanical Oscillations of magnetic strips under the influence of external field, Proceedings of JEMS 2012 – Joint European Magnetism Symposia, EPJ Web of Conferences, 40 (2013), 13004.
  12. J.M. Melenk, M. Faustmann, D. Praetorius: Efficient and robust approximation of the Helmholtz equation, Oberwolfach Reports, 9 (2012), 3305-3338.
  13. M. Aurada, M. Feischl, M. Karkulik, D. Praetorius: Adaptive coupling of FEM and BEM: Simple error estimators and convergence (IABEM 2011), IABEM 2011 Conference, Brescia, 05.09.201108.09.2011, Proceedings of IABEM 2011, (2011), S. 35-40.
  14. M. Aurada, M. Feischl, M. Karkulik, D. Praetorius: Adaptive coupling of FEM and BEM: Simple error estimators and convergence (AfriCOMP11), Proceedings of AfriCOMP11 - 2nd African Conference on Computational Mechanics (2011), #56.
  15. M. Feischl, M. Karkulik, J.M. Melenk, D. Praetorius: Residual a-posteriori error estimates in BEM: convergence of h-adaptive algorithms, IABEM 2011 Conference, Brescia, 05.09.2011-08.09.2011, Proceedings of IABEM 2011, (2011), pp. 135-140.
  16. M. Aurada, S. Ferraz-Leite, D. Praetorius: Convergence of adaptive boundary element methods, Proceedings of CMM 2009 – Computer Methods in Mechanics, 113–114.
  17. S. Ferraz-Leite, C. Ortner, D. Praetorius: Adaptive boundary element method: Simple error estimators and convergence, Oberwolfach Workshop on Analysis of Boundary Element Methods, Oberwolfach Reports, Volume 5, Issue 2 (2008).
  18. C. Ortner, D. Praetorius: A non-conforming finite element method for convex variational problems, Oberwolfach Workshop on Nonstandard Finite Element Methods, Oberwolfach Reports, Volume 5, Issue 3 (2008).
  19. C. Carstensen, S. Funken, D. Praetorius: Averaging techniques for BEM, Book of Abstracts, IABEM 2006 Conference, pp. 139–142.
  20. O. Koch, R. März, D. Praetorius, E. Weinmüller: Collocation methods for index-1 DAEs with a critical point, Oberwolfach Workshop on Differential-Algebraic Equations, Oberwolfach Reports, 18 (2006), pp. 81–84.

Scientific presentations

  • Unconditional full R-linear convergence and optimal complexity of AFEM for nonlinear PDEs [Poster (PDF)]
    3rd SFB International Workshop 2025 "Taming Complexity in Partial Differential Systems", University of Vienna, 2025 
  • Functional a-posteriori error estimates for BEM[Handout (PDF)]
    Workshop 2CCC, HU Berlin, 2024
  • Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs[Handout (PDF)]
    Plenary talk at CMAM 2024 conference, University of Bonn, 2024
  • On optimal computational costs of AFEM [Handout (PDF)]
    Workshop CC2LX, TU Wien, 2022
  • Goal-oriented adaptive FEMs with optimal computational complexity [Handout (PDF)]
    Workshop on Recent Advances in the Numerical Approximation of PDEs, University of Milan, 2021
  • Chiral magnetic skyrmions and computational micromagnetism [Handout (PDF)] 
    GAMM Seminar on Microstructures, University of Freiburg, 2020
  • Rate optimal adaptive FEM with inexact solver for nonlinear operators [Handout (PDF)]
    Workshop BI.discrete, University of Bielefeld, 2019
  • Adaptive BEM with inexact PCG solver yields almost optimal computational costs [Handout (PDF)]
    Mathematical colloquium at University of Bayreuth, 2019
  • Axioms of adaptivity revisited: Optimal adaptive IGAFEM [Handout (PDF)]
    ESI Workshop on Interplay of geometric processing, modelling, and adaptivity in Galerkin methods, Erwin-Schrödinger Institute, Wien, 2018
  • Optimal convergence rates for adaptive FEM for compactly perturbed elliptic problems [Handout (PDF)]
    Conference on Foundations of Computational Mathematics, University of Barcelona, 2017
  • AFEM with inhomogeneous Dirichlet data [Handout (PDF)]
    Central Workshop, TU Wien, 2017