Approximation of Elliptic Boundary-Value Problems Jean-Pierre Aubin

ISBN: 9780486457918

Published: February 27th 2007

Paperback

384 pages


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Approximation of Elliptic Boundary-Value Problems  by  Jean-Pierre Aubin

Approximation of Elliptic Boundary-Value Problems by Jean-Pierre Aubin
February 27th 2007 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 384 pages | ISBN: 9780486457918 | 8.62 Mb

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. Thisself-contained text for advanced undergraduates and graduateMoreA 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.



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