Journal Publikationen (peer reviewed)

  1. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab, Exponential 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]
  2. N. Angleitner, M. Faustmann, J.M. Melenk: H-inverses for RBF interpolation, Adv. Comput. Math. 49, 85 (2023). [www] [arXiv:2109.05763]
  3. 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]
  4. N. Angleitner, M. Faustmann, J.M. Melenk: Exponential meshes and H-matrices, Comput. Math. Appl., 130 (2023), 21-40. [www] [arXiv:2203.09925]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]

Proceedings

  1. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D, to appear in Proceedings of ICOSAHOM 2020+1 (2022). [arXiv:2204.04113]
  2. 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]
  3. M. Faustmann, J.M. Melenk, D. Praetorius: Efficient and Robust Approximation of the Helmholtz Equation, Oberwolfach Reports, 9 (2012), 3305-3338. [www]