An explicit a posteriori error indicator for electromagnetic, finite element-boundary integral analysis

Within the finite element method (FEM), there is always an error associated with the solution. Quantifying this error is a very important aspect of FE analysis, since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization, optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost. This paper presents an a posteriori error indicator for time-harmonic, electromagnetic analysis in three dimensions, when using a Galerkin FE approach with curl-conforming elements and including a nonlocal, boundary integral boundary condition as well as a dominant-mode port boundary condition. The error indicator is residual-based, of an explicit nature and constitutes a bound on an error energy measure. The error indicator is evaluated by presenting results relating to common microwave engineering applications, which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm.