Mixed Finite Element Approximation of Darcy's Law in Porous Media
نویسندگان
چکیده
A mixed nite element formulation for eeciently computing the velocity eld for uid ows in porous media is presented. Raviart Thomas (RT 0) and Brezzi Douglas Marini (BDM 1) spaces of lowest order are considered and compared both on analytic and realistic test cases. The BDM 1 space proves to be preferable to the simpler RT 0 with respect to CPU time and memory storage, if a xed accuracy is required. The related algebraic problem has been solved either using an Uzawa-like method with ad-hoc preconditioners or solving a penalized Lagrangian. These two approaches are comparable with the well known hybridization technique. Moreover, the precondi-tioned Uzawa system shows good convergence properties yielding a constant number of iterations versus problem size.
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