Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27120%2F18%3A10239484" target="_blank" >RIV/61989100:27120/18:10239484 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27240/18:10239484 RIV/61989100:27730/18:10239484 RIV/61989100:27740/18:10239484

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00211-017-0925-3" target="_blank" >https://link.springer.com/article/10.1007/s00211-017-0925-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00211-017-0925-3" target="_blank" >10.1007/s00211-017-0925-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem

Popis výsledku v původním jazyce

In this paper, we develop adaptive inexact versions of iterative algorithms applied to finite element discretizations of the linear Stokes problem. We base our developments on an equilibrated stress a posteriori error estimate distinguishing the different error components, namely the discretization error component, the (inner) algebraic solver error component, and possibly the outer algebraic solver error component for algorithms of the Uzawa type. We prove that our estimate gives a guaranteed upper bound on the total error, as well as a polynomial-degree-robust local efficiency, and this on each step of the employed iterative algorithm. Our adaptive algorithms stop the iterations when the corresponding error components do not have a significant influence on the total error. The developed framework covers all standard conforming and conforming stabilized finite element methods on simplicial and rectangular parallelepipeds meshes in two or three space dimensions and an arbitrary algebraic solver. Implementation into the FreeFem++ programming language is invoked and numerical examples showcase the performance of our a posteriori estimates and of the proposed adaptive strategies. As example, we choose here the unpreconditioned and preconditioned Uzawa algorithm and the preconditioned minimum residual algorithm, in combination with the Taylor-Hood discretization. (C) 2017 Springer-Verlag GmbH Deutschland

Název v anglickém jazyce

Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem

Popis výsledku anglicky

In this paper, we develop adaptive inexact versions of iterative algorithms applied to finite element discretizations of the linear Stokes problem. We base our developments on an equilibrated stress a posteriori error estimate distinguishing the different error components, namely the discretization error component, the (inner) algebraic solver error component, and possibly the outer algebraic solver error component for algorithms of the Uzawa type. We prove that our estimate gives a guaranteed upper bound on the total error, as well as a polynomial-degree-robust local efficiency, and this on each step of the employed iterative algorithm. Our adaptive algorithms stop the iterations when the corresponding error components do not have a significant influence on the total error. The developed framework covers all standard conforming and conforming stabilized finite element methods on simplicial and rectangular parallelepipeds meshes in two or three space dimensions and an arbitrary algebraic solver. Implementation into the FreeFem++ programming language is invoked and numerical examples showcase the performance of our a posteriori estimates and of the proposed adaptive strategies. As example, we choose here the unpreconditioned and preconditioned Uzawa algorithm and the preconditioned minimum residual algorithm, in combination with the Taylor-Hood discretization. (C) 2017 Springer-Verlag GmbH Deutschland

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Numerische Mathematik

ISSN

0029-599X

e-ISSN

—

Svazek periodika

134

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

1-39

Kód UT WoS článku

000428049800008

EID výsledku v databázi Scopus

2-s2.0-85035335409