Enclosure of solutions of weakly nonlinear elliptic boundary value problems and their computation
type: Item
instance of: scholarly article
title: Enclosure of solutions of weakly nonlinear elliptic boundary value problems and their computation
zbMATH Open document ID: 0681.65076
DOI: 10.1007/BF02239752
author: R. L. Voller
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: An algorithm is presented to compute approximate as well as continuous bounds for solutions of weakly nonlinear elliptic boundary value problems. The given problem is majorized in some sense and the resulting problem is solved by a finite element method. The finite element solution is computed by a monotone iteration process and finally transformed into a continuous (lower) bound for a solution. Convergence is proved and the effects of mesh refinement are discussed. Two numerical examples are given.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 4115884
zbMATH Keywords: monotone enclosure
zbMATH Keywords: weakly nonlinear elliptic boundary value problems
zbMATH Keywords: finite element method
zbMATH Keywords: monotone iteration
zbMATH Keywords: Convergence
zbMATH Keywords: mesh refinement
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02239752
OpenAlex ID: W252784379
description: scientific article; zbMATH DE number 4115884