Higher-order vector finite elements for tetrahedral cells

The finite element solution of three-dimensional electromagnetic problems using the lowest order vector finite elements, defined by Nedelec (1980) on a tetrahedra, has been well documented. However, these mixed-order elements, which allow a constant tangential, linear normal (CT/LN) representation of the fields on mesh edges, limit the accuracy of the finite element solution. Higher order basis functions, also defined by Nedelec, allow for more accurate solutions of 3D problems, while retaining the benefit of allowing no spurious modes. The next higher order basis functions on a tetrahedra provide for linear tangential, quadratic normal (LT/QN) representation of the fields. The higher order basis functions above those have a quadratic tangential, cubic normal (QT/CuN) representation of the fields. The paper describes the application of lowest order (CT/LN) and higher order (CLT/QN) vector basis functions to resonant cavity analysis and presents comparisons between the accuracy of the two methods.