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

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Published in Comptes rendus mathématique. 2011, vol. 349, no. 19-20, p. 1041-1046
Abstract 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.
Keywords Nonmonotone quasilinear elliptic problemA priori error estimatesNumerical quadratureVariational crimeFinite elements
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Research group Analyse numérique
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ABDULLE, Assyr, VILMART, Gilles. The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. In: Comptes rendus mathématique, 2011, vol. 349, n° 19-20, p. 1041-1046. https://archive-ouverte.unige.ch/unige:41942

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Deposited on : 2014-11-18

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