Expanded Mixed Finite Element Methods
نویسنده
چکیده
We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its ux (the coeecient times the gradient). Based on this formulation, mixed nite element approximations of the second-order elliptic problems are considered. Optimal order error estimates in the L p-and H ?s-norms are obtained for the mixed approximations. Various implementation techniques for solving the systems of algebraic equations are discussed. A postprocessing method for improving the scalar variable is analyzed, and superconvergent estimates in the L p-norm are derived. The mixed formulation is suitable for the case where the coeecient of diierential equations is a small tensor and does not need to be inverted.
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