Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10173889" target="_blank" >RIV/00216208:11320/13:10173889 - isvavai.cz</a>

Výsledek na webu

<a href="http://onlinelibrary.wiley.com/doi/10.1002/gamm.201310006/pdf" target="_blank" >http://onlinelibrary.wiley.com/doi/10.1002/gamm.201310006/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/gamm.201310006" target="_blank" >10.1002/gamm.201310006</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems

Popis výsledku v původním jazyce

The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE boundary value and eigenvalue problems is a numerical scheme that automatically and iteratively adapts the finite element space until a sufficiently accurate approximate solution is found. The adaptation process is based on a posteriori error estimators, and at each step of this process an algebraic problem (linear or nonlinear algebraic system or eigenvalue problem) has to be solved. In practical computations the solution of the algebraic problem cannot be obtained exactly. As a consequence, the algebraic error should be incorporated in the context of the AFEM and its a posteriori error estimators. The goal of this paper is to survey some existing approaches in the AFEM context that consider the interplay between the finite element discretization and the algebraic computation. We believe that a better understanding of this interplay is of great importance for the future development in the area of numerically

Název v anglickém jazyce

Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems

Popis výsledku anglicky

The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE boundary value and eigenvalue problems is a numerical scheme that automatically and iteratively adapts the finite element space until a sufficiently accurate approximate solution is found. The adaptation process is based on a posteriori error estimators, and at each step of this process an algebraic problem (linear or nonlinear algebraic system or eigenvalue problem) has to be solved. In practical computations the solution of the algebraic problem cannot be obtained exactly. As a consequence, the algebraic error should be incorporated in the context of the AFEM and its a posteriori error estimators. The goal of this paper is to survey some existing approaches in the AFEM context that consider the interplay between the finite element discretization and the algebraic computation. We believe that a better understanding of this interplay is of great importance for the future development in the area of numerically

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

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

GAMM Mitteilungen

ISSN

0936-7195

e-ISSN

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Svazek periodika

36

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

28

Strana od-do

102-129

Kód UT WoS článku

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EID výsledku v databázi Scopus

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