The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics)
Susanne C. Brenner,Ridgway Scott | 2007-12-14 00:00:00 | Springer | 402 | Engineering
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. This expanded second edition contains new chapters on additive Schwarz preconditioners and adaptive meshes. New exercises have also been added throughout. 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. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests.
Reviews
This is an excellent book to learn about the mathematical foundations of FEM. It is good not only for advanced (graduate) students but also the author gets to try the topic in a manner understandable also for less-expert students or researchers.
Reviews
This book certainly has a lot of information in it, but it is not lucid at all. This book is a hard read. The presentation is not done very well, and a lot of details get put off to the literature. I would actually recommend the FEM book by Braess instead. Only use this book as a reference.
Reviews
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.
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