Abstract

For modeling the vector nature of electromagnetic fields, tangential vector finite elements (TVFEs) overcome most of the shortcomings of node based finite elements. Mixed-order TVFEs offer several advantages over polynomial complete TVFEs and hierarchical TVFEs allow for mixing of different order TVFEs within a computational domain. Lowest order mixed-order TVFEs are widely used for solving electromagnetic problems but this is not the case for higher order mixed-order TVFEs. This paper provides a description of certain mixed-order TVFEs for triangular elements and presents numerical results demonstrating the merits of hierarchical mixed-order TVFEs. It is hoped that the paper will provide insight in the nature of hierarchical mixed-order TVFEs and serve as a rationale for their use.

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