On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains.
type: Item
instance of: scholarly article
title: On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains.
zbMATH Open document ID: 1066.65124
DOI: 10.1023/A:1013756310753
author: Miloslav Feistauer
author: Karel Najzar
author: V. Sobotíková
published in: Applications of Mathematics
publication date: 2005-04-19T00:00:00Z
full work available at URL: https://eudml.org/doc/33092
review text: Poisson's equation with nonlinear boundary conditions in a boun\-ded two-dimensional domain is considered. The weak solution of this problem is approximated by means of linear triangular finite elements. Using the concept of Zlámal's ideal element, the authors examine the so-called variational crimes; namely numerical integration and approximation of a piecewise curved boundary by a polygonal one. They prove the existence and uniqueness of the discrete solution, and also the convergence of the proposed finite element method in \(H^1\)-norm without any additional regularity assumptions on the true solution.
reviewed by: Michal Křížek
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 2158714
zbMATH Keywords: convergence
zbMATH Keywords: Poisson's equation
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: finite elements
zbMATH Keywords: variational crimes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2158714