Approximation of Elliptic Boundary-Value Problems

Aubin, Jean-Pierre

ISBN 10: 0486457915 / ISBN 13: 9780486457918

Published by Dover Publications, 2007

About this Item

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Bibliographic Details

• Title: Approximation of Elliptic Boundary-Value Problems
• Publisher: Dover Publications
• Publication Date: 2007
• Language: English
• ISBN 10: 0486457915
• ISBN 13: 9780486457918
• Binding: paperback
• Condition: Good

About this title

Synopsis

A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed  this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators.
The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.