Publications
- 137 journal publications (in total), 40 journal publications (plus 6 preprints) since 2020
- 32 proceedings contribution (in total), 3 proceedings contributions since 2020
- 125 publications (with 1577 citations) are listed in MathSciNet
- 145 publications (with 2067 citations, h-index 24) are listed in Scopus
- 134 publications (with 4225 citations, h-index 36) are listed on Google Scholar
- A. Bespalov, D. Praetorius, T. Round, A. Savinov: Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM, arXiv:2406.05028, 2024
- P. Bringmann, A. Miraci, D. Praetorius: Iterative solvers in adaptive FEM, arXiv:2404.07126, 2024
- A. Miraci, D. Praetorius, J. Streitberger: Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs, arXiv:2401.17778, 2024
- M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs, arXiv:2401.06486, 2024
- P. Bringmann, M. Feischl, A. Miraci, D. Praetorius, J. Streitberger: On full linear convergence and optimal complexity of adaptive FEM with inexact solver, arXiv:2311.15738, 2023
- A. Bespalov, D. Praetorius, M. Ruggeri: Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals, arXiv:2208.09388, 2022
- P. Bringmann, M. Brunner, D. Praetorius, J. Streitberger: Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs, Journal of Numerical Mathematics, accepted (2024). [arXiv:2312.00489].
- 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], [corrigendum], [arXiv:2212.00353]
- 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], arXiv:2210.10415]
- 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], [arXiv:2211.04123]
- 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], [arXiv:2101.11407]
- 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]
- 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], [arXiv:2203.06445]
- V. Helml, M. Innerberger, D. Praetorius: Plain convergence of goal-oriented adaptive FEM, Computers & Mathematics with Applications, 147 (2023), 130–149. [www], [arXiv:2208.10143]
- 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], [arXiv:2203.01845]
- 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], [arXiv:2106.15157]
- 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], [arXiv:2112.06687]
- 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]
- 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]
- 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], [arXiv:2107.02023]
- 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]
- G. Gantner, D. Praetorius: Plain convergence of adaptive algorithms without exploiting reliability and efficiency, IMA Journal of Numerical Analysis, 42 (2022), 1434–1453. [www], [arXiv:2009.01349]
- 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], [arXiv:2004.07762]
- 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], [arXiv:2107.06613]
- 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] [arXiv:2203.01845]
- 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], [arXiv:2106.03362]
- 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], [arXiv:2112.00451]
- 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]
- 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], [arXiv:2003.13270]
- 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]
- 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]
- 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]
- 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], [arXiv:2004.13137]
- 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]
- M. Innerberger, D. Praetorius: Instance-optimal goal-oriented adaptivity, Computational Methods in Applied Mathematics, 21 (2021), 109–126. [www] [arXiv:1907.13035]
- 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], [arXiv:1912.05789]
- 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]
- 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]
- 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]
- 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], [arXiv:1805.00715]
- 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], [arXiv:2005.11015]
- G. Gantner, D. Praetorius: Adaptive IGAFEM with optimal convergence rates: T-splines, Computer Aided Geometric Design, 81 (2020), #101906 (20 pages). [www], [arXiv:1910.01311]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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], [arXiv:1806.00313]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Erath, D. Praetorius: Adaptive finite volume methods with convergence rates, SIAM Journal on Numerical Analysis, 54 (2016), 2228–2255. [www], [arXiv:1508.06155]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Vogler, C. Abert, F. Bruckner, D. Süss, D. Praetorius: Basic noise mechanisms of heat-assisted magnetic recording, 120 (2016), 153901. [www]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Carstensen, M. Feischl, M. Page, D. Praetorius: Axioms of adaptivity, Computers & Mathematics with Applications, 67 (2014), 1195–1253. [www], [arXiv:1312.1171]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Page, D. Praetorius: Convergence of adaptive FEM for some elliptic obstacle problem, Applicable Analysis, 92 (2013), 595–615. [www]
- 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]
- 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]
- 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]
- M. Aurada, S. Ferraz-Leite, D. Praetorius: Estimator reduction and convergence of adaptive BEM, Applied Numerical Mathematics, 62 (2012), 787–801. [www]
- 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]
- 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]
- C. Carstensen, D. Praetorius: Convergence of adaptive boundary element methods, Journal of Integral Equations and Applications, 24 (2012), 1–23. [www]
- 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]
- S. Funken, D. Praetorius, P. Wissgott: Efficient implementation of adaptive P1-FEM in MATLAB, Computational Methods in Applied Mathematics, 11 (2011), 460–490. [www]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Carstensen, D. Praetorius: On stabilized models in micromagnetics, Computational Mechanics, 39 (2007), 663–672. [www]
- 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]
- 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]
- 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]
- 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]
- N. Popovic, D. Praetorius: H-matrix techniques for stray-field computations in computational micromagnetics, Lecture Notes in Computer Science, 3743 (2006), 102–110. [www]
- 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]
- C. Carstensen, D. Praetorius: Numerical analysis for a macroscopic model in micromagnetics, SIAM Journal on Numerical Analysis, 42 (2005), 2633–2651. [www]
- 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]
- N. Popovic, D. Praetorius: Applications of H-matrix techniques in micromagnetics, Computing, 74 (2005), 177–204. [www]
- 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]
- 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]
- D. Praetorius: Analysis of the operator ∆−1div arising in magnetic models, Zeitschrift für Analysis und ihre Anwendungen, 23 (2004), 589–605. [www]
- D. Praetorius: Remarks and examples concerning distance ellipsoids, Colloquium Mathematicum, 93 (2002), 41–53. [www]
- M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM for semilinear elliptic PDEs, Proceedings of ENUMATH 2023, accepted 2024. [preprint]
- M. Brunner, D. Praetorius, J. Streitberger: Optimal cost of (goal-oriented) adaptive FEM for general second-order linear elliptic PDEs, Proceedings of ENUMATH 2023, accepted, 2024. [preprint]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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.
- 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]
- 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]
- 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).
- 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).
- 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).
- 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).
- C. Carstensen, M. Feischl, D. Praetorius: Rate optimality of adaptive algorithms, ECCOMAS Newsletter, 07 (2014), 20–23.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- J.M. Melenk, M. Faustmann, D. Praetorius: Efficient and robust approximation of the Helmholtz equation, Oberwolfach Reports, 9 (2012), 3305-3338.
- 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.
- 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.
- 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.
- M. Aurada, S. Ferraz-Leite, D. Praetorius: Convergence of adaptive boundary element methods, Proceedings of CMM 2009 – Computer Methods in Mechanics, 113–114.
- 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).
- 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).
- C. Carstensen, S. Funken, D. Praetorius: Averaging techniques for BEM, Book of Abstracts, IABEM 2006 Conference, pp. 139–142.
- 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.