Wissenschaftliche Artikel

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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
Brunner, M., Innerberger, M., Miraçi, A., Praetorius, D., Streitberger, J., & Heid, P. (2024). Corrigendum to: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs. IMA Journal of Numerical Analysis, 44(3), 1903–1909. https://doi.org/10.1093/imanum/drad103 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
Haberl, A., Praetorius, D., Schimanko, S., & Vohralík, M. (2021). Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Numerische Mathematik, 147(3), 679–725. https://doi.org/10.1007/s00211-021-01176-w ( reposiTUm)

Beiträge in Tagungsbänden

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). ( reposiTUm)
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). ( reposiTUm)

Präsentationen

Brunner, M., Becker, R., Innerberger, M., Melenk, J. M., & Praetorius, D. (2023, September 4). Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs [Conference Presentation]. European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2023), Lissabon, Portugal. http://hdl.handle.net/20.500.12708/188566 ( reposiTUm)

Preprints

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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)
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 ( reposiTUm)