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An introduction to the finite element method. (English) Zbl 0561.65079
New York etc.: McGraw-Hill Book Company. XIII, 495 p. DM 150.45 (1984).
The book serves as a textbook for a first course in the finite element method. It is assumed that the reader has basic knowledges in linear algebra and differential equations. The purpose of the book is to teach the application rather than the theory of the finite element method. The finite element method is introduced as a variationally based technique of solving differential equations. A minimum of mathematical background (such as the development of variational formulations) is included, advanced mathematics (such as introduction of Sobolev spaces, weak solutions etc.) are avoided.
All steps of the finite element method are explained: variational formulation - approximation methods (such as those of Ritz and Galerkin) - construction of test functions (finite elements, splines) - derivation and solution of the resulting system of algebraic equations - computer implementation. Second and fourth-order ordinary differential equations, time-dependent problems as well as Laplace equations in two dimensions are considered. Representative examples from various fields (such as heat transfer, fluid and solid mechanics) are given. Nonlinear problems, shells or three-dimensional problems are not treated.
Reviewer: J.Weisel

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation