Beschreibung:
This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques.
Partial Differential Equations: Basics and Explicit Representation of Solutions.- Finite Difference Methods.- Weak Solutions, Elliptic Problems and Sobolev Spaces.- The Finite Element Method.- Finite Element Methods for Unsteady Problems.- Singular Perturbations.- Numerical Methods for Variational Inequalities and Optimal Control.- Numerical Methods for Discretized Problems.