Hierarchical hp finite elements in hybrid domains

In this paper we introduce a new set of hp finite element expansions for use in hybrid domains using hexahedrons, prisms, pyramids and tetrahedrons. The expansions are explained in terms of a unified notation which incorporates the standard hexahedral hp finite element expansion. The new bases are motivated from a set of orthogonal polynomial expansions within each of the hybrid domains. The polynomial expansions are a generalised product of functions based upon a local coordinate system with independent limits. This construction leads to expansions with attractive computational properties and which exhibit a high level of orthogonality. (C) 1997 Elsevier Science B.V.