An A Posteriori Error Estimator for a Non Homogeneous Dirichlet Problem Considering a Dual Mixed Formulation

ABSTRACT In this paper, we describe an a posteriori error analysis for a conforming dual mixed scheme of the Poisson problem with non homogeneous Dirichlet boundary condition. As a result, we obtain an a posteriori error estimator, which is proven to be reliable and locally efficient with respect to the usual norm on H d i v ; Ω × L 2 Ω. We remark that the analysis relies on the standard Ritz projection of the error, and take into account a kind of a quasi-Helmholtz decomposition of functions in H d i v ; Ω, which we have established in this work. Finally, we present one numerica...

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