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

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APPENDIX 7B

AN UNSUCCESSFUL EXAMPLE OF ADAPTIVE REFINEMENT

7B.1 INTRODUCTION

The locally normalized Z/Z error estimator defined by Eqs. 7.3 and 7.4 in the main text is used to guide the adaptive refinement of the five-element demonstration problem in this Appendix. The objective of this demonstration is twofold: (1) to show that the Runge function and its derivatives are, indeed, challenging functions to approximate and (2) to show that a usually successful error estimator can fail to produce a convergent result.

7B.2 EXAMPLE 1

Before presenting this example of a negative result, it should be noted that the error estimator defined by Eqs. 7.3 and 7.4 successfully guided the adaptive refinement procedure to an acceptable converged result for ...

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