Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Discretization Techniques Based on Domain Decomposition.- 1.1 Introduction to Mortar Finite Element Methods.- 1.2 Mortar Methods with Alternative Lagrange Multiplier Spaces.- 1.3 Discretization Techniques Based on the Product Space.- 1.4 Examples for Special Mortar Finite Element Discretizations.- 1.5 Numerical Results.- Iterative Solvers Based on Domain Decomposition.- 2.1 Abstract Schwarz Theory.- 2.2 Vector Field Discretizations.- 2.3 A Multigrid Method for the Mortar Product Space Formulation.- 2.4 A Dirichlet-Neumann Type Method.- 2.5 A Multigrid Method for the Mortar Saddle Point Formulation.- List of Figures.- List of Tables.- Notations.