Scientific Publications

Journal Publications (peer reviewed)

  1. M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab: Weighted analytic regularity for the integral fractional Laplacian in polygons, in press in SIAM J. Math. Anal. (2022). [arXiv:2112.08151]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]