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 ...