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Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element/boundary integral (FE/BI) simulation of complicated electromagnetic problems. They provide versatility in the geometrical modeling of physical structures, guarantee solutions free of spurious modes, and allow a local increase of resolution by combination of mixed-order TVFEs of different orders within a computational domain. Regions with higher order mixed-order TVFEs can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication. This paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of FE/BI solutions of electromagnetic radiation problems using hierarchical mixed-order TVFEs for tetrahedra.Index Terms-Antennas, finite-element methods (FEMs), numerical methods, tangential vector finite element.

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