Workgroup on Numerics of PDEs

Univ.Prof. Dipl.-Math. Dr.techn.Dirk Praetorius

Professor of Numerics of PDEs

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Research profile of Dirk Praetorius , opens an external URL in a new window

https://www.asc.tuwien.ac.at/praetorius/ , opens an external URL in a new window

Research interests

Our research deals with the development of numerical methods for PDEs, where we mainly consider the finite element method (FEM), the boundary element method (BEM), as well as coupled discretizations. Of recent interest are the analysis of adaptive strategies and, in particular, of the optimal interplay of local mesh-refinement and iterative solvers. Another field of expertise are numerical methods for computational micromagnetics, where we also address analytical questions like well-posedness and strong-weak uniqueness of the arising coupled PDE.

Administration

Brigitte Ecker

Administration office

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Postdocs

Projektass.(FWF) Dott. mag.Michele Alde

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Projektass.(FWF) Dipl.-Ing.Alexander FreiszlingerBSc

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Univ.Ass. Dipl.-Ing.inPaula HilbertBSc

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Student Assistants

Aleksandar DadicBSc

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Aleksandar DadicBSc

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Aleksandar DadicBSc

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Recent journal publications (since 2023)

Brunner, M., Praetorius, D., & Streitberger, J. (2025). Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs. Numerische Mathematik, 157, 409–445. https://doi.org/10.1007/s00211-025-01455-w
| Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2025). On full linear convergence and optimal complexity of adaptive FEM with inexact solver. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 180, 102–129. https://doi.org/10.1016/j.camwa.2024.12.013
| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new window

Bringmann, P. (2024). Review and computational comparison of adaptive least-squares finite element schemes. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 172, 1–15. https://doi.org/10.1016/j.camwa.2024.07.022
| Review and computational comparison of adaptive least-squares finite element schemes at reposiTUm , opens an external URL in a new window
Bringmann, P., Ketteler, J., & Schedensack, M. (2024). Discrete Helmholtz Decompositions of Piecewise Constant and Piecewise Affine Vector and Tensor Fields. Foundations of Computational Mathematics. https://doi.org/10.1007/s10208-024-09642-1
| Discrete Helmholtz Decompositions of Piecewise Constant and Piecewise Affine Vector and Tensor Fields at reposiTUm , opens an external URL in a new window
Bringmann, P., Brunner, M., Praetorius, D., & Streitberger, J. (2024). Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs. Journal of Numerical Mathematics. https://doi.org/10.1515/jnma-2023-0150
| Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P., Carstensen, C., & Streitberger, J. (2024). Local parameter selection in the C⁰ interior penalty method for the biharmonic equation. Journal of Numerical Mathematics, 32(3), 257–273. https://doi.org/10.1515/jnma-2023-0028
| Local parameter selection in the C⁰ interior penalty method for the biharmonic equation at reposiTUm , opens an external URL in a new window
Bringmann, P., Miraçi, A., & Praetorius, D. (2024). Chapter Four - Iterative solvers in adaptive FEM: Adaptivity yields quasi-optimal computational runtime. ADVANCES IN APPLIED MECHANICS, 59, 147–212. https://doi.org/10.1016/bs.aams.2024.08.002
| Chapter Four - Iterative solvers in adaptive FEM: Adaptivity yields quasi-optimal computational runtime at reposiTUm , opens an external URL in a new window
Innerberger, M., Miraçi, A., Praetorius, D., & Streitberger, J. (2024). hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis, 58(1), 247–272. https://doi.org/10.1051/m2an/2023104
| hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs at reposiTUm , opens an external URL in a new window

Helml, V., Innerberger, M., & Praetorius, D. (2023). Plain convergence of goal-oriented adaptive FEM. Computers and Mathematics with Applications, 147, 130–149. https://doi.org/10.1016/j.camwa.2023.07.022
| Plain convergence of goal-oriented adaptive FEM at reposiTUm , opens an external URL in a new window
Becker, R., Brunner, M., Innerberger, M., Melenk, J. M., & Praetorius, D. (2023). Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis, 57(4), 2193–2225. https://doi.org/10.1051/m2an/2023036
| Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new window
Brunner, M., Innerberger, M., Miraçi, A., Praetorius, D., Streitberger, J., & Heid, P. (2023). Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs. IMA Journal of Numerical Analysis, 44(3), 1560–1596. https://doi.org/10.1093/imanum/drad039
| Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs at reposiTUm , opens an external URL in a new window
Innerberger, M., & Praetorius, D. (2023). MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. Applied Mathematics and Computation, 442, Article 127731. https://doi.org/10.1016/j.amc.2022.127731
| MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P. (2023). How to prove optimal convergence rates for adaptive least-squares finite element methods. Journal of Numerical Mathematics, 31(1), 43–58. https://doi.org/10.1515/jnma-2021-0116
| How to prove optimal convergence rates for adaptive least-squares finite element methods at reposiTUm , opens an external URL in a new window
Di Fratta, G., Jüngel, A., Praetorius, D., & Slastikov, V. (2023). Spin-diffusion model for micromagnetics in the limit of long times. Journal of Differential Equations, 343, 467–494. https://doi.org/10.1016/j.jde.2022.10.012
| Spin-diffusion model for micromagnetics in the limit of long times at reposiTUm , opens an external URL in a new window
Becker, R., Gantner, G., Innerberger, M., & Praetorius, D. (2023). Goal-oriented adaptive finite element methods with optimal computational complexity. Numerische Mathematik, 153, 111–140. https://doi.org/10.1007/s00211-022-01334-8
| Goal-oriented adaptive finite element methods with optimal computational complexity at reposiTUm , opens an external URL in a new window
Di Fratta, G., Pfeiler, C.-M., Praetorius, D., & Ruggeri, M. (2023). The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics. Computational Methods in Applied Mathematics, 23(1), 145–175. https://doi.org/10.1515/cmam-2022-0060
| The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics at reposiTUm , opens an external URL in a new window

Current Preprints (since 2023)

Bringmann, P., Miraci, A., & Praetorius, D. (2024). Iterative Solvers in Adaptive FEM: Adaptivity Yields Quasi-Optimal Computational Runtime. arXiv. https://doi.org/10.48550/arXiv.2404.07126
| Iterative Solvers in Adaptive FEM: Adaptivity Yields Quasi-Optimal Computational Runtime at reposiTUm , opens an external URL in a new window
Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2024). On full linear convergence and optimal complexity of adaptive FEM with inexact solver. arXiv. https://doi.org/10.48550/arXiv.2311.15738
| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new window
Miraci, A., Praetorius, D., & Streitberger, J. (2024). Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs. arXiv. https://doi.org/10.48550/arXiv.2401.17778
| Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs at reposiTUm , opens an external URL in a new window
Brunner, M., Praetorius, D., & Streitberger, J. (2024). Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs. arXiv. https://doi.org/10.48550/arXiv.2401.06486
| Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new window

Bringmann, P., Brunner, M., Praetorius, D., & Streitberger, J. (2023). Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs. arXiv. https://doi.org/10.48550/arXiv.2312.00489
| Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs at reposiTUm , opens an external URL in a new window
Bespalov, A., Praetorius, D., & Ruggeri, M. (2023). Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals. arXiv. https://doi.org/10.48550/arXiv.2208.09388
| Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals at reposiTUm , opens an external URL in a new window

Recent talks (since 2023)

Alde, M., Feischl, M., & Praetorius, D. (2025, January 30). BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics. 24th GAMM Seminar on Microstructures 2025, Berlin, Germany.
| BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics at reposiTUm , opens an external URL in a new window

Miraci, A. (2024, December 17). Iterative solvers and optimal complexity of adaptive finite element methods. Internal Seminar at Inria (2024), Paris, France.
| Iterative solvers and optimal complexity of adaptive finite element methods at reposiTUm , opens an external URL in a new window
Bringmann, P. (2024, December 9). Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods. Seminar für Numerische Mathematik und Mechanik 2024, Essen, Germany.
| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new window
Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2024). On full linear convergence and optimal complexity of adaptive FEM with inexact solver. In Chemnitz FE-Symposium 2024 : Programme, Collection of abstracts, List of participants (pp. 52–52).
| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new window
Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2024, August 8). On full linear convergence and optimal complexity of adaptive FEM with inexact solver. 2CCC Workshop on Numerical Analysis 2024, Berlin, Germany.
| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new window
Praetorius, D., Kurz, S., Pauly, D., Repin, S., Sebastian, D., & Freiszlinger, A. (2024, August 8). Functional a-posteriori error estimates for BEM. 2CCC Workshop on Numerical Analysis 2024, Berlin, Germany.
| Functional a-posteriori error estimates for BEM at reposiTUm , opens an external URL in a new window
Bringmann, P. (2024, June 25). Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods. Workshop on Minimum Residual & Least-Squares Finite Element Methods (MINRES&LS-FEM 2024), Bilbao, Spain.
| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new window
Bringmann, P., Brunner, M., Praetorius, D., & Streitberger, J. (2024). Cost-optimal goal-oriented adaptive FEM with nested iterative solvers. In Book of Abstracts: 10th International Conference on Computational Methods in Applied Mathematics (CMAM-10) (pp. 72–72).
| Cost-optimal goal-oriented adaptive FEM with nested iterative solvers at reposiTUm , opens an external URL in a new window
Freiszlinger, A., & Praetorius, D. (2024). Convergence of adaptive multilevel stochastic Galerkin FEM for parametric PDEs. In Book of Abstracts: 10th International Conference on Computational Methods in Applied Mathematics (CMAM-10) (pp. 82–82).
| Convergence of adaptive multilevel stochastic Galerkin FEM for parametric PDEs at reposiTUm , opens an external URL in a new window
Praetorius, D., Bringmann, P., Gantner, G., Miraci, A., & Streitberger, J. (2024). Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs. In Book of Abstracts: 10th International Conference on Computational Methods in Applied Mathematics (CMAM-10) (pp. 13–13).
| Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P. (2024). Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods. In Book of Abstracts: 10th International Conference on Computational Methods in Applied Mathematics (CMAM-10) (pp. 55–55).
| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new window
Praetorius, D., Bringmann, P., Gantner, G., Miraci, A., & Streitberger, J. (2024, May 30). Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs. JAM Walkshop on Computational PDEs (2024), Jena, Germany.
| Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2024). On full linear convergence and optimal complexity of adaptive FEM with inexact solver. In Austrian Numerical Analysis Day 2024, 16– 17 May 2024: Abstracts (pp. 9–9).
| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new window
Miraci, A., Innerberger, M., Papež, J., Praetorius, D., Streitberger, J., & Vohralik, M. (2024, May 14). Role of hp-Robust Iterative Solvers in Adaptive Finite Element Algorithms for Optimal Complexity. SIAM Conference on Applied Linear Algebra (LA24), Paris, France.
| Role of hp-Robust Iterative Solvers in Adaptive Finite Element Algorithms for Optimal Complexity at reposiTUm , opens an external URL in a new window
Miraci, A. (2024, May 3). Role of hp-robust solvers in optimal complexity of AFEM. Numerical Analysis and Scientific Computing Seminar (2024), Manchester, United Kingdom of Great Britain and Northern Ireland (the).
| Role of hp-robust solvers in optimal complexity of AFEM at reposiTUm , opens an external URL in a new window
Miraci, A. (2024, April 24). Parameter-robust convergence and optimal complexity of AFEM. Seminar in the Framework of the PDE Afternoon (2024), Wien, Austria.
| Parameter-robust convergence and optimal complexity of AFEM at reposiTUm , opens an external URL in a new window
Praetorius, D., Gantner, G., Innerberger, M., Miraci, A., & Streitberger, J. (2024, February 28). Optimal complexity of adaptive FEM for nonlinear PDEs. Numerical Analysis Seminar at the University of Hongkong (2024), Hong Kong, China.
| Optimal complexity of adaptive FEM for nonlinear PDEs at reposiTUm , opens an external URL in a new window

Bringmann, P. (2023, November 16). Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods. BI.discrete23: Numerical Analysis Workshop, Bielefeld, Germany.
| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new window
Brunner, M., Becker, R., Innerberger, M., Melenk, J. M., & Praetorius, D. (2023, September 4). Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2023), Lissabon, Portugal.
| Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new window
Streitberger, J., Bringmann, P., Brunner, M., Miraci, A., & Praetorius, D. (2023, September 4). Cost-optimal goal-oriented adaptive FEM for linear elliptic PDEs. European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2023), Lissabon, Portugal.
| Cost-optimal goal-oriented adaptive FEM for linear elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P. (2023, August 31). Least-squares finite element methods - An introduction. Indian Institute of Technology Bombay (IITB): Department of Mathematics Seminar 2023, Mumbai, India.
| Least-squares finite element methods - An introduction at reposiTUm , opens an external URL in a new window
Praetorius, D., Brunner, M., Heid, P., Innerberger, M., Miraci, A., & Streitberger, J. (2023, June 13). Adaptive FEM for linear elliptic PDEs: Optimal complexity. FoCM 2023, Paris, France.
| Adaptive FEM for linear elliptic PDEs: Optimal complexity at reposiTUm , opens an external URL in a new window
Melenk, J. M., Bahr, B., Faustmann, M., Parvizi, M., & Praetorius, D. (2023, June 12). AFEM for the fractional Laplacian. Foundations of Computational Mathematics (FoCM 2023), Paris, France.
| AFEM for the fractional Laplacian at reposiTUm , opens an external URL in a new window
Brunner, M., Praetorius, D., Becker, R., Innerberger, M., & Melenk, J. M. (2023, June 8). Goal-oriented adaptivity for semilinear elliptic PDEs. Jena-Augsburg-Meeting (JAM) on Numerical Analysis, Augsburg, Germany.
| Goal-oriented adaptivity for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new window
Bringmann, P. (2023, May 3). Discontinuous least-squares finite element methods with built-in a posteriori error estimation. Forschungsseminar Numerische Mathematik der Friedrich-Schiller-Universität Jena 2023, Jena, Germany.
| Discontinuous least-squares finite element methods with built-in a posteriori error estimation at reposiTUm , opens an external URL in a new window
Streitberger, J., Brunner, M., Heid, P., Innerberger, M., Miraci, A., & Praetorius, D. (2023, April 27). Adaptive FEM for linear elliptic PDEs: optimal complexity. Austrian Numerical Analysis Day 2023, Wien, Austria.
| Adaptive FEM for linear elliptic PDEs: optimal complexity at reposiTUm , opens an external URL in a new window
Miraci, A., Brunner, M., Heid, P., Innerberger, M., Praetorius, D., & Streitberger, J. (2023, March 22). Adaptive FEM for linear elliptic PDEs: Optimal complexity. Finite Element Workshop 2023, Jena, Germany.
| Adaptive FEM for linear elliptic PDEs: Optimal complexity at reposiTUm , opens an external URL in a new window

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act	Is needed to store logged in users (marketing/tracking).	90 days	HTTP	Meta (Facebook)
_fbp	Is needed to store and track visits to various websites (marketing/tracking).	3 months	HTTP	Meta (Facebook)
datr	Is needed to identify the browser for security and website integrity purposes, including account recovery and identification of potentially compromised accounts.	2 years	HTTP	Meta (Facebook)
dpr	Is used for analysis purposes. Technical parameters are logged (e.g. aspect ratio and dimensions of the screen) so that Facebook apps can be displayed correctly.	1 week	HTTP	Meta (Facebook)
sb	Is needed to store browser details and security information of the Facebook account.	2 years	HTTP	Meta (Facebook)
dbln	Is needed to store browser details and security information of the Facebook account.	2 years	HTTP	Meta (Facebook)
spin	Is needed for promotional purposes and social campaign reporting.	session	HTTP	Meta (Facebook)
presence	Contains the "chat" status of logged in users.	1 month	HTTP	Meta (Facebook)
cppo	Is needed for statistical purposes.	90 days	HTTP	Meta (Facebook)
locale	Is needed to save the language settings.	session	HTTP	Meta (Facebook)
pl	Required for Facebook Pixel.	2 years	HTTP	Meta (Facebook)
lu	Required for Facebook Pixel.	2 years	HTTP	Meta (Facebook)
c_user	Required for Facebook Pixel.	3 months	HTTP	Meta (Facebook)
bcookie	Is needed to store browser data (marketing/tracking).	2 years	HTTP	LinkedIn
li_oatml	Is needed to identify LinkedIn members outside of LinkedIn for advertising and analytics purposes.	1 month	HTTP	LinkedIn
BizographicsOptOut	Is needed to save privacy settings.	10 years	HTTP	LinkedIn
li_sugr	Is needed to store browser data (marketing/tracking).	3 months	HTTP	LinkedIn
UserMatchHistory	Is needed to provide advertising or retargeting (marketing/tracking).	30 days	HTTP	LinkedIn
linkedin_oauth_	Is needed to provide cross-page functionality.	session	HTTP	LinkedIn
lidc	Is needed to store performed actions on the website (marketing/tracking).	1 day	HTTP	LinkedIn
bscookie	Is needed to store performed actions on the website (marketing/tracking).	2 years	HTTP	LinkedIn
X-LI-IDC	Is needed to provide cross-page functionality (marketing/tracking).	session	HTTP	LinkedIn
AnalyticsSyncHistory	Stores the time when the user was synchronized with the "lms_analytics" cookie.	30 days	HTTP	LinkedIn
lms_ads	Is needed to identify LinkedIn members outside of LinkedIn.	30 days	HTTP	LinkedIn
lms_analytics	Is needed to identify LinkedIn members for analytics purposes.	30 days	HTTP	LinkedIn
li_fat_id	Required for indirect member identification used for conversion tracking, retargeting and analytics.	30 days	HTTP	LinkedIn
U	Is needed to identify the browser.	3 months	HTTP	LinkedIn
_guid	Is needed to identify a LinkedIn member for advertising via Google Ads.	90 days	HTTP	LinkedIn

Workgroup on Numerics of PDEs

Research interests

Administration

Brigitte Ecker

Postdocs

Projektass.(FWF) Dr.rer.nat.Philipp Bringmann

Projektass.(FWF) Dipl.-Ing. Dr.techn.Maximilian BrunnerBSc

Univ.Ass.inAni MiraciPhD

Student Assistants

Recent journal publications (since 2023)

Current Preprints (since 2023)

Recent talks (since 2023)

Links

TU internal

Editorial work

Links

TU internal

Editorial work

Workgroup on Numerics of PDEs

Research interests

Administration

Brigitte Ecker

Postdocs

Projektass.(FWF) Dr.rer.nat.Philipp Bringmann

Projektass.(FWF) Dipl.-Ing. Dr.techn.Maximilian BrunnerBSc

Univ.Ass.inAni MiraciPhD

Student Assistants

Recent journal publications (since 2023)

2025

2024

2023

Current Preprints (since 2023)

2024

2023

Recent talks (since 2023)

2025

2024

2023

Links

TU internal

Editorial work

Links

TU internal

Editorial work