Elliptic Differential Equations

Theory and Numerical Treatment

Wolfgang Hackbusch (Autor)

Buch | Hardcover

XIV, 311 Seiten

1992 | 1st ed. 1992. 2nd printing 1992
Springer Berlin (Verlag)
978-3-540-54822-5 (ISBN)

Infos

Das Buch bietet eine gemeinsame Darstellung der Theorie und Numerik der elliptischen Randwertaufgaben. Zum Inhalt gehören sowohl die klassische Theorie (Greensche Darstellung, Maximumprinzip usw.) als auch die Variationsformulierung. Neben der finiten Differenzenmethode wird auch die Methode der finiten Elemente ausführlich diskutiert. Spezielle Kapitel sind den Eigenwertproblemen und der Stokes-Gleichung gewidmet.

---

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 8.10.1992
• Reihe/Serie: Springer Series in Computational Mathematics
• Übersetzer: R. Fadiman, P.D.F. Ion
• Zusatzinfo: XIV, 311 p.
• Verlagsort: Berlin
• Sprache: englisch
• Gewicht: 600 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: difference methods • Differenzenmethode • elliptic boundary value problems • Elliptische Differenzialgleichungen • elliptische Randwertprobleme • Finite Elemente • finite elements methods • Methode der finiten Elemente • Randwertprobleme • Stokes equation • Stokes-Gleichung • variational formulation • Variationsformulierung
• ISBN-10: 3-540-54822-X / 354054822X
• ISBN-13: 978-3-540-54822-5 / 9783540548225
• Zustand: Neuware