• Numerik von PDEs
  • Finite Elemente Methode (FEM)
  • Randelementmethode (BEM)
  • a-posteriori Fehlerschätzung und adaptive Netzverfeinerung
  • optimale Kopplung von Netzverfeinerung und iterativen Lösern
  • Matrixkompression und Black-Box-Vorkonditionierung durch Verwendung von hierarchischen Matrizen
  • Computational Micromagnetics

Wissenschaftliche Publikationen

  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, 198–208, 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. [pdf]
  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.

Wissenschaftliche Vorträge

  • 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