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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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