This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory.

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

Preface(2ndEd)*Preface(1stED)*Basic Concepts*Sobolev Spaces*Variational Formulation of Elliptic Boundary Value Problems*The Construction of a Finite Element of Space*Polynomial Approximation Theory in Sobolev Spaces*n-Dimensional Variational Problems*Finite Element Multigrid Methods*Additive Schwarz Preconditioners*Max-norm Estimates*Adaptive Meshes*Variational Crimes*Applications to Planar Elasticity*Mixed Methods*Iterative Techniques for Mixed Methods*Applications of Operator-Interpolation Theory*References*Index