Stability Estimates for Hybrid Coupled Domain Decomposition Methods

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. Preliminaries -- Sobolev Spaces: Saddle Point Problems