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

被引：0

作者：

Feistauer M. ^{[1
,2
]}

Najzar K. ^{[1
,2
]}

Sobotíková V. ^{[1
,2
]}

机构：

[1] Institute of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 8, 186 75

[2] Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Praha 6, 166 27

来源：

Applications of Mathematics | 2001年 / 46卷 / 5期

关键词：

Approximation of a curved boundary; Convergence of the finite element method; Elliptic equation; Finite element approximation; Ideal interpolation; Ideal triangulation; Monotone operator method; Nonlinear Newton boundary condition; Numerical integration;

D O I：

10.1023/A:1013756310753

中图分类号：

学科分类号：

摘要：

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.

引用

页码：353 / 382

页数：29

共 30 条

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