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.<>