Stability Estimates for Hybrid Coupled Domain Decomposition Methods

摘要: 1 Preliminaries 1.1 Sobolev Spaces 1.2 Saddle Point Problems 1.3 Finite Element 1.4 Projection Operators 1.5 Quasi Interpolation 2 Stability Results 2.1 Piecewise Linear Elements 2.2 Dual 2.3 Higher Order 2.4 Biorthogonal Basis Functions 3 The Dirichlet-Neumann Map for Elliptic 3.1 Steklov-Poincare Operator 3.2 Newton Potential 3.3 Approximation by Methods 3.4 Boundary 4 Mixed Discretization Schemes 4.1 Variational with Approximate 4.2 Lagrange Multiplier 5 Hybrid Coupled Domain Decomposition 5.1 Dirichlet 5.2 A Two-Level Method 5.3 Three-Field 5.4 Neumann 5.5 Numerical 5.6 Concluding Remarks References