A posteriori error estimates based on multilevel decompositions with an iterative solver on the coarsest level

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00644209" target="_blank" >RIV/67985840:_____/25:00644209 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/25:10511086

Výsledek na webu

<a href="https://doi.org/10.1553/etna_vol63s566" target="_blank" >https://doi.org/10.1553/etna_vol63s566</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1553/etna_vol63s566" target="_blank" >10.1553/etna_vol63s566</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A posteriori error estimates based on multilevel decompositions with an iterative solver on the coarsest level

Popis výsledku v původním jazyce

Multilevel methods represent a powerful approach to the numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for the total and algebraic errors of the computed approximations. This paper deals with residual-based error estimates that rely on properties of quasi-interpolation operators, stable splittings, or frames. We focus on the settings where the system matrix on the coarsest level is still large and the associated terms in the estimates can only be approximated. We show that the way in which the error term associated with the coarsest level is approximated is crucial. It can significantly affect both the efficiency (accuracy) of the overall error estimates and their robustness with respect to the size of the coarsest-level problem. We propose a new approximation of the coarsest-level term based on using the conjugate gradient method with an appropriate stopping criterion. We prove that the resulting estimates are efficient and robust with respect to the size of the coarsest-level problem. Numerical experiments illustrate the theoretical findings.

Název v anglickém jazyce

A posteriori error estimates based on multilevel decompositions with an iterative solver on the coarsest level

Popis výsledku anglicky

Multilevel methods represent a powerful approach to the numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for the total and algebraic errors of the computed approximations. This paper deals with residual-based error estimates that rely on properties of quasi-interpolation operators, stable splittings, or frames. We focus on the settings where the system matrix on the coarsest level is still large and the associated terms in the estimates can only be approximated. We show that the way in which the error term associated with the coarsest level is approximated is crucial. It can significantly affect both the efficiency (accuracy) of the overall error estimates and their robustness with respect to the size of the coarsest-level problem. We propose a new approximation of the coarsest-level term based on using the conjugate gradient method with an appropriate stopping criterion. We prove that the resulting estimates are efficient and robust with respect to the size of the coarsest-level problem. Numerical experiments illustrate the theoretical findings.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-06159S" target="_blank" >GA23-06159S: Vírové struktury: pokročilé metody identifikace a efektivní numerické simulace</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Transactions on Numerical Analysis

ISSN

1068-9613

e-ISSN

1068-9613

Svazek periodika

63

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

566-608

Kód UT WoS článku

001677407600013

EID výsledku v databázi Scopus

2-s2.0-105028260586