Geodesic
A posteriori error estimates for the 3D stabilized Mortar finite element method applied to the Laplace equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 6, pp. 991-1011.

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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates the error for the Lagrange multiplier.

DOI : 10.1051/m2an:2003064
Classification : 65N30
Keywords: Mortar finite element method, a posteriori estimates, mixed variational formulation, stabilization technique, non-matching grids 
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     author = {Belhachmi, Zakaria},
     title = {A posteriori error estimates for the $3${D} stabilized {Mortar} finite element method applied to the {Laplace} equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Belhachmi, Zakaria. A posteriori error estimates for the $3$D stabilized Mortar finite element method applied to the Laplace equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 6, pp. 991-1011. doi : 10.1051/m2an:2003064. http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003064/

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