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

Result code in 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>

Alternative codes found

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

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Publication year

2018

Confidentiality

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

Name of the periodical

Numerische Mathematik

ISSN

0029-599X

e-ISSN

—

Volume of the periodical

134

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

39

Pages from-to

1-39

UT code for WoS article

000428049800008

EID of the result in the Scopus database

2-s2.0-85035335409