Convergence of the multigrid full approximation scheme for a class of elliptic mildly nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Convergence of the multigrid full approximation scheme for a class of elliptic mildly nonlinear boundary value problems
zbMATH Open document ID: 0617.65108
DOI: 10.1007/BF01398879
author: Arnold Reusken
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133235
review text: The multigrid full approximation scheme (FAS MG) is a well-known solver for nonlinear boundary value problems. In this paper we restrict ourselves to a class of second order elliptic mildly nonlinear problems and we give local conditions, e.g. a local Lipschitz condition on the derivative of the continuous operator, under which the FAS MG with suitable chosen parameters locally converges. We prove quantitative convergence statements and deduce explicit bounds for important quantities such as the radius of a ball of guaranteed convergence, the number of smoothings needed, the number of coarse grid corrections needed and the number of FAS MG iterations needed in a nested iteration. These bounds show well-known features of the FAS MG scheme.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 4001395
zbMATH Keywords: local Lipschitz condition
zbMATH Keywords: multigrid full approximation scheme
zbMATH Keywords: second order elliptic mildly nonlinear problems
zbMATH Keywords: smoothings
zbMATH Keywords: coarse grid corrections
zbMATH Keywords: nested iteration
zbMATH Keywords: local convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4001395