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The Essentials of Finite Element Modeling and Adaptive Refinement by John O. Dow

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Chapter 1

INTRODUCTION

1.1 Problem Definition

The finite element method is capable of producing accurate approximate solutions for a wide variety of differential equations. The domain of the problem is broken into a finite number of geometrically simple subdivisions. These subdivisions, known as finite elements, are shown in Fig. 1.1. The exact solution is approximated on an individual element by low-order polynomial interpolation functions that attempt to represent the actual displacements that exist on the domain of the finite element.

ch01-f01.eps

Figure 1.1. A finite element mesh.

Errors are produced by the finite element model when the low-order ...

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