Reliability assessment of an `a posteriori´ error estimate for adaptive computation of electromagnetic field problems

Optimal performance of an adaptive finite element (FE) computation depends on the availability of a reliable and computationally efficient `a posteriori´ error estimation strategy. The reliability of an error estimate ensures that the quality of the computed solution remains within a specified accuracy and also guarantees that the error estimate applies uniformly over the entire problem domain. Reliability analysis of two different error estimates with a model problem and numerical test results are reported in this paper. A mathematical model for the reliability assessment of an `a posteriori´ error estimate through asymptotic exactness is also presented. The reliability or the performance of two different error estimates is assessed by adaptively solving a linear boundary value problem