The Mathematical Theory of Finite Element Methods

Rating:
Summary: a nice introductory book
Review: This book is a very nice introductory book on the subject. It has a very nice presentation of the fundamental issues on finite element theory, such as interpolation theory on Sobolev spaces and variational formulations of elliptic problems. Also, it covers some advanced and more specific subjets such as multigrid methods and mixed methods for fluid mechanics, where it reviews some of the most used techniques to solve the saddle-point problems such as Augmented Lagrangian techniques and penalty methods.

Also, at the end of the book there is a very well written chapter focused on Interpolation operators, where there is a very nice (and very easy to read) presentation of the Sccot-Zhang interpolation operator, and some of the principal results on approximation.

Resuming, it is a very recomendable book in the subjet, specially recomendable for mathematics students interested on finite elements, and researchers in the field.