| Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
|---|---|---|
| Page(s) | 247 - 272 | |
| DOI | https://doi.org/10.1051/m2an/2023104 | |
| Published online | 16 February 2024 | |
hp-Robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
TU Wien, Institute of Analysis and Scientific Computing, Wiedner Hauptstr. 8-10/E101/4, 1040 Vienna, Austria
* Corresponding author: julian.streitberger@asc.tuwien.ac.at
Received:
21
February
2023
Accepted:
18
December
2023
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that the iterative solver contracts the algebraic error robustly with respect to the polynomial degree p ≥ 1 and the (local) mesh size h. We further prove that the built-in algebraic error estimator which comes with the solver is hp-robustly equivalent to the algebraic error. The application of the solver within the framework of adaptive finite element methods with quasi-optimal computational cost is outlined. Numerical experiments confirm the theoretical findings.
Mathematics Subject Classification: 65N12 / 65N30 / 65N55 / 65Y20
Key words: Adaptive finite element method / local multigrid / hp-robustness / stable decomposition
© The authors. Published by EDP Sciences, SMAI 2024
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