Stability Estimates for Hybrid Coupled Domain Decomposition Methods (Paperback)

Preliminaries. - Sobolev Spaces: Saddle Point Problems; Finite Element Spaces; Projection Operators; Quasi Interpolation Operators. - Stability Results: Piecewise Linear Elements; Dual Finite Element Spaces; Higher Order Finite Element Spaces; Biorthogonal Basis Functions. - The Dirichlet-Neumann Map for Elliptic Problems: The Steklov-Poincare Operator; The Newton Potential; Approximation by Finite Element Methods; Approximation by Boundary Element Methods. - Mixed Discretization Schemes: Variational Methods with Approximate Steklov-Poincare Operators; Lagrange Multiplier Methods. - Hybrid Coupled Domain Decomposition Methods: Dirichlet Domain Decomposition Methods; A Two-Level Method; Three-Field Methods; Neumann Domain Decomposition Methods; Numerical Results; Concluding Remarks. - References.