Elliptic Differential Equations: Theory and Numerical Treatment: 18 (Springer Series in Computational Mathematics) - Hardcover

Hackbusch, Wolfgang

Hardcover

ISBN 10: 354054822X ISBN 13: 9783540548225

Verlag: Springer, 2003

Inhaltsangabe

Book by Hackbusch Wolfgang

Über diesen Titel

Reseña del editor

This book has developed from lectures that the author gave for mathematics students at the Ruhr-Universitat Bochum and the Christian-Albrechts-Uni­ versitat Kiel. This edition is the result of the translation and correction of the German edition entitled Theone und Numenk elliptischer Differential­ gleichungen. The present work is restricted to the theory of partial differential equa­ tions of elliptic type, which otherwise tends to be given a treatment which is either too superficial or too extensive. The following sketch shows what the problems are for elliptic differential equations. A: Theory of B: Discretisation: c: Numerical analysis elliptic Difference Methods, convergence, equations finite elements, etc. stability Elliptic Discrete boundary value equations f-------- ----- problems E:Theory of D: Equation solution: iteration Direct or with methods iteration methods The theory of elliptic differential equations (A) is concerned with ques­ tions of existence, uniqueness, and properties of solutions. The first problem of VI Foreword numerical treatment is the description of the discretisation procedures (B), which give finite-dimensional equations for approximations to the solu­ tions. The subsequent second part of the numerical treatment is numerical analysis (0) of the procedure in question. In particular it is necessary to find out if, and how fast, the approximation converges to the exact solution.

Reseña del editor

The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He introduces the variational formulation of boundary value problems together with the necessary background from functional analysis and describes the finite element method including the most important error estimates. A more advanced chapter leads the reader into the theory of regularity. The reader will also find more details about the discretisation of singularly perturbed equations and eigenvalue problems. The author discusses the Stokes problem as an example of a saddle point problem taking into account its relevance to applications in fluid dynamics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2003
• ISBN 10: 354054822X
• ISBN 13: 9783540548225
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 2
• Anzahl der Seiten: 332