Synopses & Reviews
This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.
J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
This mathematics-oriented text features extensive discussion of Sobolev and Hilbert spaces and the theory of distributions.
This introduction to the basic mathematical theory of the finite element method is geared toward readers with limited mathematical backgrounds. Its coherent demonstrations explain the use of these techniques in developing the theory of finite elements, with detailed proofs of the major theorems and numerous examples. 1976 edition.
This introduction to the theory of Sobolev spaces and Hilbert space methods demonstrates the use of these techniques in finite element approximations of linear partial differential equations. 1976 edition.
Table of Contents
1. Introduction2. Distributions, Mollifiers, and Mean Functions3. Theory of Sobolev Spaces4. Hilbert Space Theory of Traces and Intermediate Spaces5. Some Elements of Elliptic Theory6. Finite-Element Interpolation7. Variational Boundary-Value Problems8. Finite-Element Approximations of Elliptic Boundary-Value Problems9. Time-Dependent ProblemsAuthor IndexSubject Index