Hierarchal scalar and vector tetrahedra

Abstract

A novel set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchical, allowing mixing of polynomial orders. Scalar orders up to three and vector orders up to two are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. The scalar and vector elements can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50-Hz problems: the Bath cube and the TEAM Workshop problem 7.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>