Distribution of the discretization and algebraic error in numerical solution of partial differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286559" target="_blank" >RIV/00216208:11320/14:10286559 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/14:00428023

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.laa.2014.02.009" target="_blank" >http://dx.doi.org/10.1016/j.laa.2014.02.009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2014.02.009" target="_blank" >10.1016/j.laa.2014.02.009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Distribution of the discretization and algebraic error in numerical solution of partial differential equations

Popis výsledku v původním jazyce

In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary valuemodel problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is notrestricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere.

Název v anglickém jazyce

Distribution of the discretization and algebraic error in numerical solution of partial differential equations

Popis výsledku anglicky

In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary valuemodel problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is notrestricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere.

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach<br>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

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

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Svazek periodika

449

Číslo periodika v rámci svazku

15 May 2014

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

89-114

Kód UT WoS článku

000336699600008

EID výsledku v databázi Scopus

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