The Mathematical Theory of Finite Element Methods
By: by Susanne C. Brenner, L. Ridgway Scott
Contributors: Scott, L. Ridgway
Edition: Second Edition.
Series: Texts in Applied Mathematics -- 15; Texts in applied mathematics -- 15.
Publisher: Springer New York
Published: 2002
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 363
ISBN-13: 9781475736601; 9781475736588
Subjects: Functional analysis; Mathematics; Engineering; Computer science; Applied Mechanics
Description: 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. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Review of earlier edition: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995)
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Table of contents: title: Preface(2nd ed.); title: Preface(1st ed.); title: Basic Concepts; title: Sobolev Spaces; title: Variational Formulation of Elliptic Boundary Value Problems; title: The Construction of a Finite Element of Space; title: Polynomial Approximation Theory in Sobolev Spaces; title: n-Dimensional Variational Problems; title: Finite Element Multigrid Methods; title: Additive Schwarz Preconditioners; title: Max-norm Estimates; title: Adaptive Meshes; title: Variational Crimes; title: Applications to Planar Elasticity; title: Mixed Methods; title: Iterative Techniques for Mixed Methods; title: Applications of Operator-Interpolation Theory; title: References; title: Index.