A non-overlapping domain decomposition method for parabolic initial-boundary value problems
type: Item
instance of: scholarly article
title: A non-overlapping domain decomposition method for parabolic initial-boundary value problems
zbMATH Open document ID: 0924.65094
DOI: 10.1016/S0168-9274(98)00053-1
author: Hannes Müller
author: Gert Lube
author: F. C. Otto
published in: Applied Numerical Mathematics
publication date: 1999-11-02T00:00:00Z
review text: Application of a non-overlapping domain decomposition method to a time dependent advection-reaction-diffusion model is the main goal of this paper. A discontinuous Galerkin method in time and a stabilized Galerkin method in space are the basic discretizations. For the continuous elliptic problems arising in each time step a convergence proof is available in appropriate Sobolev norms. The numerical convergence rate is independent of the mesh size. Several numerical examples in two space variables with exact solutions are included and the time dependent discrete relative \(L_2\) errors are presented. Finally the proposed approach can be extended for more complex (also nonlinear) problems as can be shown at the end of this paper.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1311281
zbMATH Keywords: non-overlapping domain decomposition method
zbMATH Keywords: advection-reaction-diffusion model
zbMATH Keywords: parabolic initial boundary value problems
zbMATH Keywords: Galerkin method
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: Q4263448
cites work: An accelerated domain decomposition procedure based on Robin transmission conditions
cites work: Adaptive domain decomposition methods for advection dominated equations
cites work: Q3973650
cites work: Q4303877
cites work: Stabilized finite element methods for singularly perturbed parabolic problems
cites work: FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM
cites work: A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE OSEEN EQUATIONS
cites work: Q4864111
cites work: A new finite element formulation for computational fluid dynamics. IX: Fourier analysis of space-time Galerkin/least-squares algorithms
cites work: Q4360234
full work available at URL: s0168-9274(98)00053-1
OpenAlex ID: W1995187808
description: scientific article; zbMATH DE number 1311281