Expanded mixed finite element methods for linear second-order elliptic problems, I
نویسنده
چکیده
We develop a new mixed formulation for the numencal solution of second-order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are exphcitly treated the scalar unknown, its gradient, and its flux (the coefficient times the gradient) Based on this formulation, mixed finite element approximations of the second-order elliptic problems are considered Optimal order error estimâtes in the L~ and H~ -norms are obtained for the mixed approximations. Vanous implementation techniques for solving the Systems of algebraic équations are discussed A postprocessing method for improving the scalar variable is analyzed, and superconvergent estimâtes in the L-norm are denved The mixed formulation is suitable for the case where the coefficient of differential équations is a small tensor and does not need to be inverted © Elsevier, Paris Résumé —L'objet de cet article est l'écriture d'une nouvelle formulation mixte relative aux problèmes elliptiques d'ordre deux, et l'implémentation de méthodes d'éléments finis mixtes pour la détermination de solutions approchées On donne alors des estimations d'erreurs en norme L et H~ s Enfin, on construit une méthode pour laquelle des résultats de superconvergence en norme îf sont obtenus © Elsevier, Pans
منابع مشابه
Expanded mixed finite element methods for quasilinear second order elliptic problems, II
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