ON THE EFFECT OF NUMERICAL INTEGRATION IN THE FINITE ELEMENT SOLUTION OF AN ELLIPTIC PROBLEM WITH A NONLINEAR NEWTON BOUNDARY CONDITION
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
ON THE EFFECT OF NUMERICAL INTEGRATION IN THE FINITE ELEMENT SOLUTION OF AN ELLIPTIC PROBLEM WITH A NONLINEAR NEWTON BOUNDARY CONDITION
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
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Volume of the periodical
64
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
39
Pages from-to
129-167
UT code for WoS article
000463984700003
EID of the result in the Scopus database
2-s2.0-85064208805