Finite element method. Vol. 1: The basis.
type: Item
instance of: scholarly article
zbMATH Open document ID: 0991.74002
author: Oleg C. Zienkiewicz
author: R. L. Taylor
publication date: 2001-04-23T00:00:00Z
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 76-02
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1589895
zbMATH Keywords: point based methods
zbMATH Keywords: triangular elements
zbMATH Keywords: rectangular elements
zbMATH Keywords: non-conforming elements
zbMATH Keywords: infinite elements
zbMATH Keywords: stress
zbMATH Keywords: strain
zbMATH Keywords: deformation
zbMATH Keywords: linear elasticity
zbMATH Keywords: fluid mechanics
zbMATH Keywords: heat conduction
zbMATH Keywords: boundary value problem
zbMATH Keywords: discretization
zbMATH Keywords: error estimation
zbMATH Keywords: convergence
zbMATH Keywords: finite element method
zbMATH Keywords: linear problems
zbMATH Keywords: adaptive error control
zbMATH Keywords: meshless methods
MaRDI profile type: Publication
title: Finite element method. Vol. 1: The basis.
review text: For many years continuum mechanics elaborated models of media and methods of finding solutions on the basis of these models. The abilities of engineers to solve the resulting boundary value problems were restricted to a comparatively small set of problems either having analytic solutions or approximate solutions within reasonable amounts of computation. Computers changed not only the viewpoint from which numerical methods could be exploited, but also the choice of mathematical models relevant to applications. The set of practical models grew, as did the set of practical problems whose solutions computer found with a good accuracy. In the pre-computer era, the main problem of continuous mechanics was to formulate boundary value problems for the corresponding systems of partial differential equations; now the emphasis has shifted to the development of finite models that accurately describe space-distributed objects while taking into account the great complexity of material properties. In this sense the finite element method (FEM) has many advantages, because it embeds and inherits all the results of the continuum theory and enhances our abilities to solve new industrial problems. However, the use of the finite element method (or better, methods, since several modifications exist) is often far from the use of a ``black box'' program where a user can simply push a button and get a result. For accurate solution of complex problems it is necessary to understand the background of FEM and the domain of its applicability. NEWLINENEWLINENEWLINEThe book under consideration is one of the most valuable sources of such information for practitioners. Generations of engineers and researchers learned FEM techniques from Zienkiewicz's books [for the review of the previous editions see Zbl 0435.73072, Zbl 0974.76003, Zbl 0974.76004, Zbl 0979.74002, Zbl 0979.74003]. They are classics in the area. This one, written with R. L. Taylor, summarizes the results of renowned authors. Practical…
reviewed by: Leonid Lebedev
description: scientific article