Flux Recovery from Primal Hybrid Finite Element Methods

Abstract

A flux recovery technique is introduced and analyzed for the computed solution of the primal hybrid finite element method for second-order elliptic problems. The recovery is carried out over a single element at a time while ensuring the continuity of the flux across the interelement edges and the validity of the discrete conservation law at the element level. Our construction is general enough to cover all degrees of polynomials and grids of triangular or quadrilateral type. We illustrate the principle using the Raviart--Thomas spaces, but other well-known related function spaces such as the Brezzi--Douglas--Marini (BDM) or Brezzi--Douglas--Fortin--Marini (BDFM) space can be used as well. An extension of the technique to the nonlinear case is given. Numerical results are presented to confirm the theoretical results.