Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F09%3A00157046" target="_blank" >RIV/68407700:21340/09:00157046 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

Popis výsledku v původním jazyce

We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order RT space linked with meshdual to the original simplicial one. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideasof local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimat

Název v anglickém jazyce

Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

Popis výsledku anglicky

We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order RT space linked with meshdual to the original simplicial one. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideasof local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimat

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

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

ISSN

0764-583X

e-ISSN

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Svazek periodika

2009

Číslo periodika v rámci svazku

43

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

22

Strana od-do

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Kód UT WoS článku

000268974800003

EID výsledku v databázi Scopus

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