Graded mesh refinement and error estimates of higher order for DGFE solutions of elliptic boundary value problems in polygons

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10128842" target="_blank" >RIV/00216208:11320/12:10128842 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1002/num.20668" target="_blank" >http://dx.doi.org/10.1002/num.20668</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/num.20668" target="_blank" >10.1002/num.20668</a>

Result language

angličtina

Original language name

Graded mesh refinement and error estimates of higher order for DGFE solutions of elliptic boundary value problems in polygons

Original language description

Error estimates for DGFE solutions are well investigated if one assumes that the exact solution is sufficiently regular. In this article, we consider a Dirichlet and a mixed boundary value problem for a linear elliptic equation in a polygon. It is well known that the first derivatives of the solutions develop singularities near reentrant corner points or points where the boundary conditions change. On the basis of the regularity results formulated in Sobolev-Slobodetskii spaces and weighted spaces of Kondratiev type, we prove error estimates of higher order for DGFE solutions using a suitable graded mesh refinement near boundary singular points. The main tools are as follows: regularity investigation for the exact solution relying on general results for elliptic boundary value problems, error analysis for the interpolation in Sobolev-Slobodetskii spaces, and error estimates for DGFE solutions on special graded refined meshes combined with estimates in weighted Sobolev spaces. Our main

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/GA201%2F08%2F0012" target="_blank" >GA201/08/0012: Qualitative analysis and numerical solution of flow problems</a><br>

Continuities

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

Publication year

2012

Confidentiality

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

Name of the periodical

Numerical Methods for Partial Differential Equations

ISSN

0749-159X

e-ISSN

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Volume of the periodical

28

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

28

Pages from-to

1124-1151

UT code for WoS article

000303052000002

EID of the result in the Scopus database

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