On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains

Miloslav Feistauer; Karel Najzar; Veronika Sobotíková

Applications of Mathematics (2001)

  • Volume: 46, Issue: 5, page 353-382
  • ISSN: 0862-7940

Abstract

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The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed.

How to cite

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Feistauer, Miloslav, Najzar, Karel, and Sobotíková, Veronika. "On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains." Applications of Mathematics 46.5 (2001): 353-382. <http://eudml.org/doc/33092>.

@article{Feistauer2001,
abstract = {The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed.},
author = {Feistauer, Miloslav, Najzar, Karel, Sobotíková, Veronika},
journal = {Applications of Mathematics},
keywords = {elliptic equation; nonlinear Newton boundary condition; monotone operator method; finite element approximation; approximation of a curved boundary; numerical integration; ideal triangulation; ideal interpolation; convergence of the finite element method; convergence; Poisson's equation; nonlinear boundary conditions; finite elements; variational crimes},
language = {eng},
number = {5},
pages = {353-382},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains},
url = {http://eudml.org/doc/33092},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Feistauer, Miloslav
AU - Najzar, Karel
AU - Sobotíková, Veronika
TI - On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 5
SP - 353
EP - 382
AB - The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed.
LA - eng
KW - elliptic equation; nonlinear Newton boundary condition; monotone operator method; finite element approximation; approximation of a curved boundary; numerical integration; ideal triangulation; ideal interpolation; convergence of the finite element method; convergence; Poisson's equation; nonlinear boundary conditions; finite elements; variational crimes
UR - http://eudml.org/doc/33092
ER -

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