| Abstract: |
| A high order flux-conservative finite element scheme is proposed and analyzed for the fluid flow models in porous media. This scheme is based on the classical Galerkin finite element method enhanced by a flux approximation on the boundary of a prescribed set of control volumes. The numerical approximations can be characterized as the solution of a constrained-minimization problem with constraints given by the flux conservation equations for each control element. It is shown that both the finite element solution and the numerical flux converge to the exact solutions with optimal orders. The theoretical results are verified by numerical experiments on test problems for which exact solutions are known. A simplified two-phase fluid flow model in porous media has been simulated to illustrate the motivation and the efficiency of this work. The numerical results match the underlying physics and hence show that the high-order conservative fluxes obtained by the scheme perform well. |
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