A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps
Result description
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.
Keywords
multigrid methoda posteriori error estimatestable decomposition
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Scientific Computing
ISSN
1064-8275
e-ISSN
1095-7197
Volume of the periodical
43
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
"S117"-"S145"
UT code for WoS article
000712863700006
EID of the result in the Scopus database
2-s2.0-85103871828
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2021