Publications

2026
B. Gräßle and SA. Sauter:
BEM for variable coefficient second-order problems,
arXiv:2605.22159, 2026. [bibtex] [doi]
B. Gräßle and SA. Sauter:
Dirichlet-to-Neumann operator for the Helmholtz problem with general wavenumbers on the n-sphere,
Accepted in Partial Differential Equations and Applications, 2026. [bibtex] [doi]
B. Gräßle:
Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements,
arXiv:2604.21887, 2026. [bibtex] [doi]
C. Carstensen, B. Gräßle and Q. Zhai:
Higher-order guaranteed lower biharmonic eigenvalue bounds,
Computer Methods in Applied Mechanics and Engineering, volume 451:118617, 2026. [bibtex] [doi]
2025
B. Gräßle, R. Hiptmair and SA. Sauter:
Stable skeleton integral equations for general coefficient Helmholtz transmission problems,
arXiv:2507.00991, 2025. [bibtex] [doi]
B. Gräßle:
Optimal trace norms for Helmholtz problems,
arXiv:2506.11944, 2025. [bibtex] [doi]
C. Carstensen, B. Gräßle and E. Pirch:
Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes,
Computer Methods in Applied Mechanics and Engineering, volume 433:117477, 2025. [bibtex] [doi]
NE. Bohne, B. Gräßle and SA. Sauter:
Pressure-improved Scott–Vogelius type elements,
Calcolo, volume 62:8, pp. 33, 2025. [bibtex] [doi]
C. Carstensen and B. Gräßle:
Adaptive Morley FEM for 2D stationary Navier-Stokes,
Mathematics of Computation, volume 95, pp. 613–645, 2025. [bibtex] [doi]
C. Carstensen and B. Gräßle:
Optimal convergence rates of adaptive WOPSIP from superclose nonconforming FEM,
Mathematics of Computation, volume 95, pp. 1187–1224, 2025. [bibtex] [doi]
B. Gräßle:
A posteriori nonconforming finite element error analysis for fourth-order problems with quadratic semilinearity,
PhD thesis, Humboldt-Universität zu Berlin, 2025. [bibtex]
2024
C. Carstensen, B. Gräßle and N. Nataraj:
Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation,
Journal of Numerical Mathematics, volume 32, pp. 77–109, 2024. [bibtex] [doi]
C. Carstensen, B. Gräßle and N. Nataraj:
A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity,
SIAM Journal on Numerical Analysis, volume 62, pp. 919–945, 2024. [bibtex] [doi]
C. Carstensen and B. Gräßle:
Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains,
Computer Methods in Applied Mechanics and Engineering, volume 425:116931, 2024. [bibtex] [doi]
C. Carstensen, B. Gräßle and NT. Tran:
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds,
Numerische Mathematik, volume 156, pp. 813–851, 2024. [bibtex] [doi]
B. Gräßle, NE. Bohne and SA. Sauter:
The pressure-wired Stokes element: a mesh-robust version of the Scott–Vogelius element,
Numerische Mathematik, volume 156, pp. 1781–1807, 2024. [bibtex] [doi]
B. Gräßle:
AFEM.jl (v0.1), 2024. [bibtex] [doi]
2023
F. Bertrand, C. Carstensen, B. Gräßle and NT. Tran:
Stabilization-free HHO a posteriori error control,
Numerische Mathematik, volume 154, pp. 369–408, 2023. [bibtex] [doi]
2022
B. Gräßle:
Conforming multilevel FEM for the biharmonic equation,
PhD thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2022. [bibtex] [doi]
B. Gräßle:
Optimal multilevel adaptive FEM for the Argyris element,
Computer Methods in Applied Mechanics and Engineering, volume 399:115352, 2022. [bibtex] [doi]