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2003 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Stability Estimates for Hybrid Coupled Domain Decomposition Methods

verfasst von: Olaf Steinbach

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Mathematics

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Introduction
Abstract
Abstract not available
Olaf Steinbach
1. Preliminaries
Abstract
  • 1.1 Sobolev Spaces
  • 1.2 Saddle Point Problems
  • 1.3 Finite Element Spaces
  • 1.4 Projection Operators
  • 1.5 Quasi Interpolation Operators
Olaf Steinbach
2. Stability Results
Abstract
  • 2.1 Piecewise Linear Elements
  • 2.2 Dual Finite Element Spaces
  • 2.3 Higher Order Finite Element Spaces
  • 2.4 Biorthogonal Basis Functions
Olaf Steinbach
3. The Dirichlet-Neumann Map for Elliptic Boundary Value Problems
Abstract
  • 3.1 The Steklov-Poincaré Operator
  • 3.2 The Newton potential
  • 3.3 Approximation by Finite Element Methods
  • 3.4 Approximation by Boundary Element Methods
Olaf Steinbach
4. Mixed Discretization Schemes
Abstract
  • 4.1 Variational Methods with Approximate Steklov-Poincaré Operators
  • 4.2 Lagrange Multiplier Methods
Olaf Steinbach
5. Hybrid Coupled Domain Decomposition Methods
Abstract
  • 5.1 Dirichlet Domain Decomposition Methods
  • 5.2 A Two-Level Method
  • 5.3 Three-Field Methods
  • 5.4 Neumann Domain Decomposition Methods
  • 5.5 Numerical Results
  • 5.6 Concluding Remarks
Olaf Steinbach
References
Abstract
Abstract not available
Olaf Steinbach
Backmatter
Metadaten
Titel
Stability Estimates for Hybrid Coupled Domain Decomposition Methods
verfasst von
Olaf Steinbach
Copyright-Jahr
2003
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-36250-0
Print ISBN
978-3-540-00277-2
DOI
https://doi.org/10.1007/b80164