Hierarchal triangular edge elements using orthogonal polynomials

Edge elements are vector finite elements that have degrees of freedom associated with their edges. Unlike nodal elements, they impose continuity only on the tangential component of the vector field, allowing the normal component to be discontinuous from one element to the next. They have been widely used for representing the electric or magnetic field in the computational analysis of electromagnetic wave problems, having distinct advantages over their nodal counterparts. The performance here of a new vector element is broadly similar to that of the corresponding scalar element, which has been applied up to order 11 for scalar electromagnetic wave problems. The new element, then, is suitable for use in a p-adaptive finite-element program for 2D vector wave problems. Moreover, a similar approach may be used to derive the p/sup th/-order tetrahedral element for application in 3D electromagnetics.