A new hierarchical basis with a minimum number of unknowns on a mesh of hexahedra for the T-Ψ edge element eddy current method

A new set of hierarchical hexahedral edge elements is presented. The new elements give up to second-order approximations both for the magnetic field and the current density. For a given polynomial order, they are more economical than the serendipity family of nodal elements. On a given mesh, increasing the polynomial order of the edge element used, improves the accuracy both for local and global quantities, but an element which is first-order complete in both fields is the most economical.