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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

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Czech description

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Type

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

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>

Continuities

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

Publication year

2013

Confidentiality

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

Name of the periodical

GAMM Mitteilungen

ISSN

0936-7195

e-ISSN

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Volume of the periodical

36

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

28

Pages from-to

102-129

UT code for WoS article

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EID of the result in the Scopus database

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