Goal-Oriented Error Estimates for hp-Adaptive Solutions of the Time-Harmonic Maxwell's Equations

We present two kinds of goal-oriented error estimates for finite element (FE) solutions of the vector Helmholtz equation on tetrahedral meshes. The error estimates are based on the dual-weighted residual (DWR) method together with hierarchical basis functions and hierarchical grids, respectively. The purpose of the two estimates is to estimate the effects of p-refinement and h-refinement, respectively. Together this gives information to determine not only which elements to refine in an iterative refinement process, but also whether these should be p-refined (increasing polynomial order p) or h-refined (reducing element size h by dividing the element into smaller elements)