by Victor B. Oliari, Paulo Rafael Bosing, Denise de Siqueira, Philippe R.B. Devloo, presented at XLII Ibero-Latin-American Congress on Computational Methods in Engineering (CILAMCE-2021) | 3rd Pan American Congress on Computational Mechanics, Novermber 2021.
We present 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 gradient of the numerical solution, with a boundary continuous restriction that comes from a smoothing process applied to the trace of the numerical solution over the mesh skeleton. The equilibrated flux is the solution of a local mixed form problem with a Neumann boundary condition given by the Lagrange multiplier of the hybrid finite element method solution. To establish the a posteriori estimates we divide the error into conforming and non-conforming parts. For the former one, a slight modification of the a posteriori error estimate proposed by Vohral ́ık  is applied, whilst the latter is bounded by the difference of the gradient of the numerical solution and the reconstructed potential. Numerical results performed in the environment PZ Devloo , show the efficiency of this strategy when it is applied for some test model problems.