Workgroup on Numerics of PDEs
Univ.Prof. Dipl.-Math. Dr.techn. Dirk Praetorius
Professor of Numerics of PDEs
Phone: +43 1 58801 10150 Call Dirk Praetorius
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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
Phone: +43 1 58801 10117 Call Brigitte Ecker
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Postdocs
Projektass.(FWF) Dr.rer.nat. Philipp Bringmann
Send email to Philipp Bringmann
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Projektass.(FWF) Dipl.-Ing. Dr.techn. Maximilian Brunner BSc
Send email to Maximilian Brunner
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Univ.Ass.in Ani Miraci PhD
Phone: +43 1 58801 10156 Call Ani Miraci
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Univ.Ass. Dr.techn. Julian Streitberger BSc MSc
Numerics of PDEs (Prof. PRAETORIUS)
Phone: +43 1 58801 10156 Call Julian Streitberger
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PhD students
Projektass.(FWF) Dott.mag. Michele Alde
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Projektass.(FWF) Dipl.-Ing. Alexander Freiszlinger BSc
Phone: +43 1 58801 10156 Call Alexander Freiszlinger
Send email to Alexander Freiszlinger
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Student Assistants
Recent journal publications (since 2023)
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| hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs at reposiTUm , opens an external URL in a new windowInnerberger, 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, opens an external URL in a new window
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| Plain convergence of goal-oriented adaptive FEM at reposiTUm , opens an external URL in a new windowHelml, 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, opens an external URL in a new window
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| Local parameter selection in the C⁰ interior penalty method for the biharmonic equation at reposiTUm , opens an external URL in a new windowBringmann, P., Carstensen, C., & Streitberger, J. (2023). Local parameter selection in the C0 interior penalty method for the biharmonic equation. Journal of Numerical Mathematics. https://doi.org/10.1515/jnma-2023-0028, opens an external URL in a new window
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| Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new windowBecker, 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, opens an external URL in a new window
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| Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs at reposiTUm , opens an external URL in a new windowBrunner, 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, opens an external URL in a new window
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| MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs at reposiTUm , opens an external URL in a new windowInnerberger, 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, opens an external URL in a new window
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| How to prove optimal convergence rates for adaptive least-squares finite element methods at reposiTUm , opens an external URL in a new windowBringmann, 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, opens an external URL in a new window
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| Spin-diffusion model for micromagnetics in the limit of long times at reposiTUm , opens an external URL in a new windowDi 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, opens an external URL in a new window
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| Goal-oriented adaptive finite element methods with optimal computational complexity at reposiTUm , opens an external URL in a new windowBecker, 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, opens an external URL in a new window
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| 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 windowDi 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, opens an external URL in a new window
Current Preprints (since 2023)
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| Iterative Solvers in Adaptive FEM: Adaptivity Yields Quasi-Optimal Computational Runtime at reposiTUm , opens an external URL in a new windowBringmann, 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, opens an external URL in a new window
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| On full linear convergence and optimal complexity of adaptive FEM with inexact solver at reposiTUm , opens an external URL in a new windowBringmann, 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, opens an external URL in a new window
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| 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 windowMiraci, A., Praetorius, D., & Streitberger, J. (2024). Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs. arXiv.
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| Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new windowBrunner, 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, opens an external URL in a new window
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| Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs at reposiTUm , opens an external URL in a new windowBringmann, 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, opens an external URL in a new window
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| Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals at reposiTUm , opens an external URL in a new windowBespalov, 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, opens an external URL in a new window
Recent talks (since 2023)
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| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new windowBringmann, 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.
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| Optimal interplay of adaptive mesh-refinement and iterative solvers for elliptic PDEs at reposiTUm , opens an external URL in a new windowPraetorius, 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.
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| Role of hp-robust solvers in optimal complexity of AFEM at reposiTUm , opens an external URL in a new windowMiraci, 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).
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| Parameter-robust convergence and optimal complexity of AFEM at reposiTUm , opens an external URL in a new windowMiraci, A. (2024, April 24). Parameter-robust convergence and optimal complexity of AFEM. Seminar in the Framework of the PDE Afternoon (2024), Wien, Austria.
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| Optimal complexity of adaptive FEM for nonlinear PDEs at reposiTUm , opens an external URL in a new windowPraetorius, 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.
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| Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods at reposiTUm , opens an external URL in a new windowBringmann, 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.
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| Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new windowBrunner, 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.
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| Cost-optimal goal-oriented adaptive FEM for linear elliptic PDEs at reposiTUm , opens an external URL in a new windowStreitberger, 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.
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| Least-squares finite element methods - An introduction at reposiTUm , opens an external URL in a new windowBringmann, P. (2023, August 31). Least-squares finite element methods - An introduction. Indian Institute of Technology Bombay (IITB): Department of Mathematics Seminar 2023, Mumbai, India.
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| Adaptive FEM for linear elliptic PDEs: Optimal complexity at reposiTUm , opens an external URL in a new windowPraetorius, 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.
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| AFEM for the fractional Laplacian at reposiTUm , opens an external URL in a new windowMelenk, 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.
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| Goal-oriented adaptivity for semilinear elliptic PDEs at reposiTUm , opens an external URL in a new windowBrunner, 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.
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| Discontinuous least-squares finite element methods with built-in a posteriori error estimation at reposiTUm , opens an external URL in a new windowBringmann, 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.
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| Adaptive FEM for linear elliptic PDEs: optimal complexity at reposiTUm , opens an external URL in a new windowStreitberger, 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.
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| Adaptive FEM for linear elliptic PDEs: Optimal complexity at reposiTUm , opens an external URL in a new windowMiraci, 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.