# A posteriori error estimates for primal hybrid finite element methods

## Palavras-chave:

FEM, Primal Hybrid, A Posteriori Error Estimate## Resumo

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 L

2

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 [1] 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 [2], show the efficiency of this strategy when it

is applied for some test model problems.