
Elliptic Differential Equations
Theory and Numerical Treatment
Wolfgang Hackbusch(Author)
Springer (Publisher)
Published on 22. March 2010
Book
Paperback/Softback
XIV, 311 pages
978-3-642-05244-6 (ISBN)
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Description
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.
More details
Series
Edition
1st. ed. 1992. 2nd printing 2010. Softcover reprint of the original 1st ed. 1992
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XIV, 311 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
1020 gr
ISBN-13
978-3-642-05244-6 (9783642052446)
DOI
10.1007/978-3-642-11490-8
Schweitzer Classification
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Persons
Content
1 Partial Differential Equations and Their Classification Into Types.- 2 The Potential Equation.- 3 The Poisson Equation.- 4 Difference Methods for the Poisson Equation.- 5 General Boundary Value Problems.- 6 Tools from Functional Analysis.- 7 Variational Formulation.- 8 The Method of Finite Elements.- 9 Regularity.- 10 Special Differential Equations.- 11 Eigenvalue Problems.- 12 Stokes Equations.