Additive Schwarz algorithms for parabolic problems
type: Item
instance of: scholarly article
title: Additive Schwarz algorithms for parabolic problems
zbMATH Open document ID: 1169.65095
author: Jing Qiang
published in: Applied Mathematics and Computation
publication date: 2009-03-10T00:00:00Z
review text: The paper deals with the solution of systems of linear algebraic equations that arise from symmetric linear parabolic finite element problems. The additive Schwarz domain decomposition methods for parabolic differential equations is introduced and also the dependence of convergence rates of these algorithms on parameters of time step and space-mesh is considered. The resulting preconditioned linear system of equations is solved by the conjugate gradient method. The author analyzes the error caused by the conjugate gradient method, namely he proves the convergence and the error estimates. Additionally to the backward Euler method also the Crank-Nicolson scheme is considered. Finally, a numerical example is enclosed.
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 5527464
zbMATH Keywords: additive Schwarz method
zbMATH Keywords: parabolic equation
zbMATH Keywords: domain decomposition
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: condition numbers
zbMATH Keywords: preconditioning
zbMATH Keywords: finite element
zbMATH Keywords: convergence
zbMATH Keywords: algorithms
zbMATH Keywords: error estimates
zbMATH Keywords: backward Euler method
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: numerical example
reviewed by: Vit Dolejsi
MaRDI profile type: Publication
full work available at URL: j.amc.2008.12.045
OpenAlex ID: W2133600821
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cites work: Additive Schwarz methods for parabolic problems
DOI: 10.1016/J.AMC.2008.12.045
description: scientific article; zbMATH DE number 5527464