An Introduction to the Mathematical Theory of Finite Elements

An Introduction to the Mathematical Theory of Finite Elements offers a clear and accessible entry into the essential concepts underlying finite element approximations. Designed with readers of modest mathematical backgrounds in mind, this self-contained text bridges the gap between fundamental theory and practical application in the treatment of partial differential equations. Developed from the authors’ extensive seminars and courses, the book is the collaborative work of J. T. Oden, Director of the Institute for Computational Engineering & Sciences at the University of Texas at Austin, and J. N. Reddy, Professor of Engineering at Texas A&M University. The text begins with introductory discussions of distributions, Sobolev spaces, and variational boundary value problems before progressing to in-depth analyses of finite element interpolation and methods for elliptic and initial boundary value problems. Detailed proofs of major theorems and numerous examples throughout the 446 pages ensure a comprehensive understanding of finite element theory.