Numerical Treatment of Partial Differential Equations

2007
ISBN: 978-3-540-71582-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 596 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 914 g

Reihe: Universitext

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.

Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.

Zielgruppe

Research

Autoren/Hrsg.

Grossmann, Christian

Stynes, Martin

Roos, Hans-Görg

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.