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Numerical Solutions of Partial Differential Equations by the Finite Element Method

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Overview


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.
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Product Details

  • ISBN-13: 9780486469003
  • Publisher: Dover Publications
  • Publication date: 1/15/2009
  • Series: Dover Books on Mathematics Series
  • Pages: 288
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.70 (d)

Table of Contents


Preface to the Dover Edition
Preface
Introduction
Introduction to FEM for elliptic problems
Abstract formulation of the finite element method for elliptic problems
Some finite element spaces
Approximation theory for FEM. Error estimates for elliptic problems
Some applications to elliptic problems
Direct methods for solving linear systems of equations
Minimization algorithms. Iterative methods
FEM for parabolic problems
Hyperbolic problems
Boundary element methods
Mixed finite element methods
Curved elements and numerical integration
References
Index
 
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