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Article Dans Une Revue Comptes rendus hebdomadaires des séances de l'Académie des sciences Année : 2011

The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods

Résumé

A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a-priori error estimates for the $H^1$ and the $L^2$ norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Our results permit the analysis of numerical homogenization methods.
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hal-00772086 , version 1 (10-01-2013)

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Assyr Abdulle, Gilles Vilmart. The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Comptes rendus hebdomadaires des séances de l'Académie des sciences, 2011, 349, pp.1041-1046. ⟨10.1016/j.crma.2011.09.005⟩. ⟨hal-00772086⟩
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