Synopses & Reviews
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Synopsis
This accessible introduction offers the keys to an important technique in computational mathematics. It outlines clear connections with applications and considers numerous examples from a variety of specialties. 1987 edition.
Synopsis
This accessible introduction offers the keys to an important technique in computational mathematics. It outlines clear connections with applications and considers numerous examples from a variety of specialties. 1987 edition.
About the Author
Claes Johnson is Professor of Applied Mathematics at the Royal Institute of Technology, Stockholm.
Table of Contents
Preface to the Dover EditionPrefaceIntroductionIntroduction to FEM for elliptic problemsAbstract formulation of the finite element method for elliptic problemsSome finite element spacesApproximation theory for FEM. Error estimates for elliptic problemsSome applications to elliptic problemsDirect methods for solving linear systems of equationsMinimization algorithms. Iterative methodsFEM for parabolic problemsHyperbolic problemsBoundary element methodsMixed finite element methodsCurved elements and numerical integrationReferencesIndex