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Stability Estimates for Hybrid Coupled Domain Decomposition Methods : Lecture Notes in Mathematics - Olaf Steinbach
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Stability Estimates for Hybrid Coupled Domain Decomposition Methods

By: Olaf Steinbach

Paperback | 1 March 2003

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1 Preliminaries1.1 Sobolev Spaces1.2 Saddle Point Problems1.3 Finite Element Spaces1.4 Projection Operators1.5 Quasi Interpolation Operators2 Stability Results2.1 Piecewise Linear Elements2.2 Dual Finite Element Spaces2.3 Higher Order Finite Element Spaces2.4 Biorthogonal Basis Functions3 The Dirichlet-Neumann Map for Elliptic Problems3.1 The Steklov-Poincare Operator3.2 The Newton Potential3.3 Approximation by Finite Element Methods3.4 Approximation by Boundary Element Methods4 Mixed Discretization Schemes4.1 Variational Methods with Approximate Steklov-Poincare Operators4.2 Lagrange Multiplier Methods5 Hybrid Coupled Domain Decomposition Methods5.1 Dirichlet Domain Decomposition Methods5.2 A Two-Level Method5.3 Three-Field Methods5.4 Neumann Domain Decomposition Methods5.5 Numerical Results5.6 Concluding Remarks References

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