A posteriori error estimates for primal hybrid finite element methods applied to Poisson problem

Abstract

This paper presents a new fully computable a posteriori error estimates for the primal hybrid finite element methods based on equilibrated flux and potential reconstructions. The reconstructed potential is obtained from a local L2 orthogonal projection of the numerical solution on a continuous function space over the mesh skeleton. The equilibrated flux is the solution of a local mixed problem with a Neumann boundary condition given by the Lagrange multipliers of the primal hybrid finite element solution. For that, a divergence-consistent finite element pair is used. The upper and lower bounds of the error estimator are proved, and numerical results illustrate the efficiency of the error indicators.