Generalized h-p triangles and tetrahedra for adaptive finite element analysis in parallel processing environments

New families of triangle and tetrahedron elements are proposed for h-p adaptive finite element analysis (AFEA) in parallel processing computational environments. The elements are constructed based on very-high-order arbitrarily piecewise-continuous polynomial bases, which span the full range of local mesh refinements, and a very broad variety of the primary local distributions of degrees of freedom (DOF), that are provided by conventional and irregular h-p adaptive refinements. Irregular-cut continuity constraints are used to maintain the conformity and modeling integrity of the new h-p elements on the external edges (faces) of the triangles (tetrahedra), to permit the seamless introduction and use of the elements within conventional AFEA formulations. The potential benefits, and related costs, of these new elements are investigated for electromagnetics applications.