Domain decomposition and splitting methods for mortar mixed finite element approximations to parabolic equations
type: Item
instance of: scholarly article
title: Domain decomposition and splitting methods for mortar mixed finite element approximations to parabolic equations
zbMATH Open document ID: 1010.65037
author: Stéphanie Gaiffe
author: Roland Masson
author: Roland Glowinski
published in: Numerische Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The method considered in this paper combines the mortar mixed finite element domain decomposition spatial discretization with projection schemes for the time discretization, in order to obtain a fully parallel algorithm for parabolic equations. This method enables also the use of hybrid meshes and local time stepping. Two versions of the time discretization by operator splitting are presented. For both schemes unconditional stability is proved and for the incremental version convergence holds true if the condition \( O ( \Delta t / h^{1/2 }) \) is true. The main advantage of this method is to be fully parallel. A numerical example with well-known exact solution is presented and the convergence history of the error in \(L_2(\Omega)\) norm for the incremental scheme is involved.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1837411
zbMATH Keywords: parabolic equations
zbMATH Keywords: domain decomposition
zbMATH Keywords: mortar mixed finite element method
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: error estimates
zbMATH Keywords: parallel computation
zbMATH Keywords: hybrid meshes
zbMATH Keywords: local time stepping
zbMATH Keywords: operator splitting
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s002110100367
OpenAlex ID: W4238741608
DOI: 10.1007/S002110100367
description: scientific article; zbMATH DE number 1837411