hp-approximation theory for BDFM and RT finite elements on quadrilaterals

摘要

We study approximation proper-ties of hp-finite element subspaces of H(div, Omega) and H(rot, Omega) on a polygonal domain Q using Brezzi Douglas-Fortin-Marini (BDFM) or Raviart-Thomas (RT) elements. Approximation theoretic results are derived for the hp-version finite element method on non-quasi-uniform meshes of quadrilateral elements with hanging nodes for functions belonging to weighted Sobolev spaces H-omega(s,l) (Omega) and the countably normed spaces B-w(l) (Omega). These results culminate in a proof of the characteristic exponential convergence property of the hp-version finite element method on suitably designed meshes under similar conditions needed for the analysis of the H-1 (Omega) case. By way of illustration, exponential convergence rates are deduced for mixed hp-approximation of flow in porous media. [References: 23]