ON THE EFFECT OF NUMERICAL INTEGRATION IN THE FINITE ELEMENT SOLUTION OF AN ELLIPTIC PROBLEM WITH A NONLINEAR NEWTON BOUNDARY CONDITION

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403978" target="_blank" >RIV/00216208:11320/19:10403978 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c9lYfVVxil" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c9lYfVVxil</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2019.0192-18" target="_blank" >10.21136/AM.2019.0192-18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

ON THE EFFECT OF NUMERICAL INTEGRATION IN THE FINITE ELEMENT SOLUTION OF AN ELLIPTIC PROBLEM WITH A NONLINEAR NEWTON BOUNDARY CONDITION

Popis výsledku v původním jazyce

This paper is concerned with the analysis of the finite element method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained by numerical integration. The theoretical results are verified by numerical experiments.

Název v anglickém jazyce

ON THE EFFECT OF NUMERICAL INTEGRATION IN THE FINITE ELEMENT SOLUTION OF AN ELLIPTIC PROBLEM WITH A NONLINEAR NEWTON BOUNDARY CONDITION

Popis výsledku anglicky

This paper is concerned with the analysis of the finite element method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained by numerical integration. The theoretical results are verified by numerical experiments.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-01747S" target="_blank" >GA17-01747S: Teorie a numerická analýza sdružených problémů dynamiky tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

64

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

39

Strana od-do

129-167

Kód UT WoS článku

000463984700003

EID výsledku v databázi Scopus

2-s2.0-85064208805