Benedikt Grässle

Forschung

• Numerical analysis of partial differential equations
• Integral equations for transmission problems
• Development and implementation of fast solvers
• Galerkin and non-standard finite element methods (FEM)
• High-precision computation of eigenvalue problems
• A posteriori error analysis and numerical verification
• Convergence analysis of adaptive schemes

List of Publications

Preprints

Bohne, N.-E., B. Gräßle and S. A. Sauter
Pressure-improved Scott-Vogelius type elements
2024. arXiv: 2403.04499 [cs, math].  http://arxiv.org/abs/2403.04499.

2025

Carstensen, C., B. Gräßle and E. Pirch
‘Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes’
Computer Methods in Applied Mechanics and Engineering 433:117477 (2025). https://linkinghub.elsevier.com/retrieve/pii/S004578252400731X.

2024

Carstensen, C. and B. Gräßle
‘Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains’
Computer Methods in Applied Mechanics and Engineering 425:116931 (2024). https://linkinghub.elsevier.com/retrieve/pii/S0045782524001877.

Carstensen, C., B. Gräßle and N. Nataraj
‘A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity’
SIAM Journal on Numerical Analysis 62.2 (2024), pp. 919–945. https://epubs.siam.org/doi/10.1137/23M1589852.

Carstensen, C., B. Gräßle and N. Nataraj
‘Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation’
Journal of Numerical Mathematics 32.1 (2024), pp. 77–109. https://www.degruyter.com/document/doi/10.1515/jnma-2022-0092/html.

Carstensen, C., B. Gräßle and N. T. Tran
‘Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds’
Numerische Mathematik 156.3 (2024), pp. 813–851. https://link.springer.com/10.1007/s00211-024-01407-w.

Gräßle, B., N.-E. Bohne and S. Sauter
‘The pressure-wired Stokes element: a mesh-robust version of the Scott–Vogelius element’
Numerische Mathematik 156.5 (2024), pp. 1781–1807. https://link.springer.com/10.1007/s00211-024-01430-x.

2023

Bertrand, F., C. Carstensen, B. Gräßle and N. T. Tran
‘Stabilization-free HHO a posteriori error control’
Numerische Mathematik 154.3-4 (2023), pp. 369–408. https://link.springer.com/10.1007/s00211-023-01366-8.

2022

Gräßle, B.
‘Conforming multilevel FEM for the biharmonic equation’
MA thesis. Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2022. http://dx.doi.org/10.18452/24833.

Gräßle, B.
‘Optimal multilevel adaptive FEM for the Argyris element’
Computer Methods in Applied Mechanics and Engineering 399:115352 (2022). https://linkinghub.elsevier.com/retrieve/pii/S0045782522004352.