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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

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/GA201%2F08%2F0012" target="_blank" >GA201/08/0012: Kvalitativní analýza a numerické řešení problémů proudění</a><br>

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Numerical Methods for Partial Differential Equations

ISSN

0749-159X

e-ISSN

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Svazek periodika

28

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

1124-1151

Kód UT WoS článku

000303052000002

EID výsledku v databázi Scopus

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