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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2014

Confidentiality

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

Name of the periodical

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

—

Volume of the periodical

281

Issue of the periodical within the volume

November 2014

Country of publishing house

CH - SWITZERLAND

Number of pages

16

Pages from-to

184-199

UT code for WoS article

000343841400008

EID of the result in the Scopus database

—