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

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CHAPTER 4

THE SOURCE AND QUANTIFICATION OF DISCRETIZATION ERRORS

4.1 INTRODUCTION

When a finite element model cannot capture the exact solution, interelement jumps or discontinuities exist in the approximate strain representation. In this chapter, we will show that these jumps directly relate to the failure of the finite element representation contained in the individual finite elements to satisfy the governing differential equation being solved. The differences between the exact solution and the finite element result are called discretization errors. These errors get their name from the fact that they occur when the continuum is replaced by a discrete number of finite elements, which, in general, cannot represent the exact solution.

The relationship ...

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