A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps

0548860 - MÚ 2022 RIV US eng J - Journal Article
Miraçi, A. - Papež, Jan - Vohralík, M.
A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps.
SIAM Journal on Scientific Computing. Roč. 43, č. 5 (2021), S117-S145. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : multigrid method * a posteriori error estimate * stable decomposition
OECD category: Pure mathematics
Impact factor: 2.968, year: 2021
Method of publishing: Limited access
https://doi.org/10.1137/20M1349503

We develop a multigrid solver steered by an a posteriori estimator of the algebraic error. We adopt the context of a second-order elliptic diffusion problem discretized by conforming finite elements of arbitrary polynomial degree p >= 1. Our solver employs zero pre- and one postsmoothing by the overlapping Schwarz (block-Jacobi) method and features an optimal choice of the step-sizes in the smoothing correction on each level by line search. This leads to a simple Pythagorean formula of the algebraic error in the next step in terms of the current error and levelwise and patchwise error reductions. We show the following two results and their equivalence: the solver contracts the algebraic error independently of the polynomial degree p, and the estimator represents a two-sided p-robust bound on the algebraic error.
Permanent Link: http://hdl.handle.net/11104/0324907