Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00431616" target="_blank" >RIV/67985840:_____/14:00431616 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cma.2014.08.005" target="_blank" >http://dx.doi.org/10.1016/j.cma.2014.08.005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2014.08.005" target="_blank" >10.1016/j.cma.2014.08.005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension

Popis výsledku v původním jazyce

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary dimension. Theestimator provides a guaranteed upper bound on the energy norm of the error and it is robust for all values of the reaction coefficient, including the singularly perturbed case. The approach is based on robustly equilibrated boundary flux functions of Ainsworth and Oden (2000) and on subsequent robust and explicit flux reconstruction. This paper simplifies and extends the applicability of the previous result of Ainsworth and Vejchodsky (2011) in three aspects: (i) arbitrary dimension, (ii) mixed boundary conditions, and (iii) non-constant reaction coefficient. It is the first robust upper bound on the error with these properties.

Název v anglickém jazyce

Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension

Popis výsledku anglicky

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary dimension. Theestimator provides a guaranteed upper bound on the energy norm of the error and it is robust for all values of the reaction coefficient, including the singularly perturbed case. The approach is based on robustly equilibrated boundary flux functions of Ainsworth and Oden (2000) and on subsequent robust and explicit flux reconstruction. This paper simplifies and extends the applicability of the previous result of Ainsworth and Vejchodsky (2011) in three aspects: (i) arbitrary dimension, (ii) mixed boundary conditions, and (iii) non-constant reaction coefficient. It is the first robust upper bound on the error with these properties.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

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Svazek periodika

281

Číslo periodika v rámci svazku

November 2014

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

16

Strana od-do

184-199

Kód UT WoS článku

000343841400008

EID výsledku v databázi Scopus

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