Stability Estimates for Hybrid Coupled Domain Decomposition Methods

Olaf Steinbach

126 pages, parution le 18/02/2003

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Résumé

Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods.

Contents

Introduction

1 Preliminaries

Sobolev Spaces
Saddle Point Problems
Finite Element Spaces
Projection Operators
Quasi Interpolation Operators

2 Stability Results

Piecewise Linear Elements
Dual Finite Element Spaces
Higher Order Finite Element Spaces
Biorthogonal Basis Functions

3 The Dirichlet-Neumann Map for Elliptic Boundary Value

Problems
The Steklov-Poincaré Operator
The Newton potential
Approximation by Finite Element Methods
Approximation by Boundary Element Methods

4 Mixed Discretization Schemes

Variational Methods with Approximate Steklov-Poincaré
Operators
Lagrange Multiplier Methods

5 Hybrid Coupled Domain Decomposition Methods

Dirichlet Domain Decomposition Methods
A Two-Level Method
Three-Field Methods
Neumann Domain Decomposition Methods
Numerical Results
Concluding Remarks

L'auteur - Olaf Steinbach

University of Stuttgart, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Olaf Steinbach
Parution	18/02/2003
Nb. de pages	126
Format	15,5 x 23,5
Couverture	Broché
Poids	199g
Intérieur	Noir et Blanc
EAN13	9783540002772