Aktuelle Forschungsfelder

  • Numerik von PDEs
  • Finite Elemente Methoden, Randelementemethoden
  • Elliptische Regularität
  • Fraktionale Differentialoperatoren
  • Hierarchische Matrizen

Preprints

  • B.Bahr, M. Faustmann, J.M. Melenk, An implementation of hp-FEM for the fractional Laplacian, arXiv:2407.11482, 2024
  • M. Faustmann, C. Marcati, J.M. Melenk, Ch. Schwab, Weighted analytic regularity for the integral fractional Laplacian in polyhedra, arXiv:2307.11679, 2023
  • M. Faustmann, A. Rieder, Fractional Diffusion in the full space: decay and regularity, arXiv:2301.05503, 2023

Publications (peer reviewed)

  1. M. Faustmann, A. Rieder, FEM-BEM coupling in Fractional Diffusion, accepted for publication in IMA Journal of Numerical Analysis. [arXiv:2302.11279]
  2. M. Faustmann, C. Marcati, J.M. Melenk, C. SchwabExponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons, SIAM Journal on Numerical Analysis, 61(6) (2023), 2601-2622. [www] [arXiv:2209.11468]
  3. N. Angleitner, M. Faustmann, J.M. Melenk: H-inverses for RBF interpolationAdv. Comput. Math. 49, 85 (2023). [www] [arXiv:2109.05763]
  4. M. Faustmann, E.P. Stephan, D. Wörgötter: Two-level error estimation for the integral fractional Laplacian, Comput. Methods Appl. Math. 23 (2023), no. 3, 603–621. [www] [arXiv:2209.13366]
  5. N. Angleitner, M. Faustmann, J.M. Melenk: Exponential meshes and H-matrices, Comput. Math. Appl., 130 (2023), 21-40. [www] [arXiv:2203.09925]
  6. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Weighted analytic regularity for the integral fractional Laplacian in polygons, SIAM J. Math. Anal., 54 (2022), 6323-6357. [www] [arXiv:2112.08151]
  7. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D, contribution in Proceedings of ICOSAHOM 2020+1, Springer LCSE 137 (2022), 291-306. [www] [arXiv:2204.04113]
  8. M. Faustmann, J.M. Melenk, M. Parvizi: H-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equation, Advances in Computational Mathematics, 48 (2022), article number: 59. [www] [arXiv:2103.14981]
  9. M. Faustmann, M. Karkulik, J.M. Melenk: Local convergence of the FEM for the integral fractional Laplacian, SIAM Journal on Numerical Analysis, 60 (2022), 1055-1082. [www] [arXiv:2005.14109]
  10. M. Faustmann, J.M. Melenk, M. Parvizi: Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings, Numerische Mathematik, 150 (2022), 849-892. [www] [arXiv:2008.11498]
  11. M. Faustmann, J.M. Melenk, M. Parvizi: On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion, Mathematical Modelling and Numerical Analysis (M2AN), 55 (2021), 595-625. [www] [arXiv:1912.09160]
  12. M. Faustmann, J.M. Melenk, D. Praetorius: Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian, Mathematics of Computation, 90 (2021), 1557-1587. [www] [arXiv:1903.10409]
  13. N. Angleitner, M. Faustmann, J. Melenk: Approximating inverse FEM matrices on non-uniform meshes with H-matrices, Calcolo, 3 (2021), 1-36. [www] [arXiv:2005.04999]
  14. M. Faustmann, J.M. Melenk: Local convergence of the boundary element method on polyhedral domains, Numerische Mathematik, 140 (3) (2018), 593-637. [www] [arXiv:1702.04224]
  15. M. Faustmann, J.M. Melenk: Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains, Computers & Mathematics with Applications, 74 (2017), 1576-1589. [www] [arXiv:1610.09211]
  16. 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]
  17. 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]
  18. 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]
  19. 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]

Vorträge

  1. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Exponential convergence of hp-FEM for the integral fractional Laplacian, 29th Biennial Conference on Numerical Analysis, Glasgow, 27.06.2023-30.06.2023.
  2. M. Faustmann, A.Rieder: FEM-BEM coupling in Fractional Diffusion, Nonlocal Equations: Analysis and Numerics, Bielefeld, 06.03.2023-10.03.2023.
  3. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Weighted analytic regularity and hp-FEM for the integral fractional Laplacian, Chemnitz FE Symposium 2022, Herrsching, 15.09.2022-17.09.2022.
  4. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Weighted analytic regularity for the integral fractional Laplacian in polygons, CMAM, Vienna, 29.08.2022-02.09.2022.
  5. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Analytic Regularity and hp-FEM for the Integral Fractional Laplacian, 19th European Finite Element Fair, Espoo, Finland, 03.06.2022-04.06.2022.
  6. B. Bahr, M. Faustmann, J.M. Melenk, D. Praetorius: Adaptive FEM for fractional diffusion, ESI Workshop , Adaptivity, High Dimensionality and Randomness, Wien, 04.04.2022-08.04.2022.
  7. M. Faustmann, M. Karkulik, J.M. Melenk, D. Praetorius: Finite Element Method for Fractional Diffusion - Recent Results, DMV-ÖMG Jahrestagung 2021, Passau, 27.09.2021-01.10.2021.
  8. M. Faustmann, M. Karkulik, J.M. Melenk, M. Parvizi, D. Praetorius: The Fractional Laplacian - Adaptive FEM, Preconditioning and Local Errors (invited talk), USM Seminar, Valparaiso (online), 29.10.2020.
  9. M. Faustmann, J.M. Melenk, M. Karkulik: Local convergence of the FEM for the integral fractional Laplacian, 4th Conference on Numerical Methods for Fractional-Derivative Problems, Peking (online), 22.10.2020-24.10.2020.
  10. M. Faustmann, J.M. Melenk, M. Parvizi, D. Praetorius: Optimal adaptivity and preconditioning for the fractional Laplacian, 15th Austrian Numerical Analysis Day, Graz, 09.05.2019-10.05.2019.
  11. M. Faustmann, J.M. Melenk, M. Parvizi, D. Praetorius: Optimal adaptivity and preconditioning for the fractional Laplacian, GAMM 2019, Wien, 18.02.2019-22.02.2019.
  12. M. Faustmann, J.M. Melenk, M. Parvizi, D. Praetorius: Optimal adaptivity and preconditioning for the fractional Laplacian, WONAPDE 2019 - Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Concepción, 21.01.2019-25.01.2019.
  13. M. Faustmann, J.M. Melenk, D. Praetorius: Optimal adaptivity for the fractional Laplacian (invited talk), Universität Bonn, Bonn, 29.11.2018.
  14. M. Faustmann, J.M. Melenk: Discrete interior regularity and applications, RMMM 8 - Reliable Methods of Mathematical Modeling, Berlin, 31.07.2017-03.08.2017.
  15. M. Faustmann, J.M. Melenk: Local convergence of the boundary element method on polyhedral domains, BEM on the Saar 2017, Saarbrücken, 29.05.2017-31.05.2017.
  16. M. Faustmann, J.M. Melenk: Local convergence of the boundary element method on polyhedral domains, 13th Austrian Numerical Analysis Day, Salzburg, 04.05.2017-05.05.2017.
  17. M. Faustmann, J.M. Melenk: Local error estimates and convergence of the Galerkin boundary element method on polygonal domains, MAFELAP 2016 - The Mathematics of Finite Elements and Applications, London, 14.06.2016-17.06.2016.
  18. M. Faustmann, J. Melenk, D. Praetorius: H-matrix approximation to the inverses of BEM matrices (invited talk), Workshop on Boundary Elements and Adaptivity, Basel, 14.03.2016-15.03.2016.
  19. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator, 11th Austrian Numerical Analysis, Linz, 06.05.2015-08.05.2015.
  20. M. Faustmann, J.M. Melenk, D. Praetorius: Black-Box Preconditioning of FEM/BEM Matrices by H-Matrix Techniques, MAFELAP 2013 - The Mathematics of Finite Elements and Applications, Uxbridge, 11.06.2013-14.06.2013.
  21. M. Faustmann, J.M. Melenk, D. Praetorius: H-Matrix approximability of inverse FEM matrices for various boundary conditions, 9th Austrian Numerical Analysis Day, Graz, 11.04.2013-12.04.2013.
  22. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H-matrix approximants to inverse BEM matrices, 10th Söllerhaus Workshop on Fast Boundary Element Methods in Industrial Applications, Hirschegg, 27.09.2012-30.09.2012.
  23. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H-matrix approximants to the inverse of BEM matrices, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Wien, 10.09.2012-14.09.2012.
  24. M. Faustmann, J.M. Melenk, D. Praetorius: Existence of H-Matrix Approximants to the Inverse of BEM Matrices, ICOSAHOM 2012, Gammarth, Tunesien, 25.06.2012-29.06.2012.

M. Faustmann: Wie das Dezimalsystem nach Europa kam, Hauptvortrag: TUforMath, Wien, 25.04.2019.