Existence and convergence of a discontinuous Galerkin method for the compressible three-phase flow problem in porous media
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This paper presents and analyzes a discontinuous Galerkin method for the compressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well-posed, and obtain a priori error estimates. Our numerical results validate the theoretical results, i.e. the algorithm converges with first order, under different setups that involve variable density and effects of gravity.
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