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Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday

Victor Ginting, University of Wyoming
On the Application of the Continuous Galerkin Finite Element Method for Solving Multiphase Flow Problems


One major drawback that prevents the use of the standard continuous Galerkin finite element method in solving conservation problems is its lack of a locally conservative flux. We present a simple post-processing for the continuous Galerkin finite element method resulting in a locally conservative flux. The post-processing requires an auxiliary fully Neumann problem to be solved independently on each finite element. Its performance is demonstrated through numerical examples of multi-phase flow in subsurface formation with triangular and quadrilateral elements along. This is a joint work with Lawrence Bush of the University of Wyoming.