Convergence of a finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary unknowns. Well-posedness is obtained in []. Theoretical convergence is proved via a compactness argument. The numerical phase saturation converges strongly to a weak solution in L² in space and in time whereas the numerical phase pressures converge strongly to weak solutions in L² in space almost everywhere in time. The proof is not straightforward because of the degeneracy of the phase mobilities and the unboundedness of the derivative of the capillary pressure.

中文翻译：

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退化多孔介质中两相流的有限元方法。第二部分：融合

为了解决多孔介质中不相溶的两相流问题，提出了一种具有质量集总和通量上风的有限元方法的收敛性。该方法直接近似润湿相压力和饱和度，这是主要未知数。在[]中获得适定性。理论上的收敛性通过紧密性论证得到证明。数值相饱和度在时间和空间上都强烈收敛于L ²的弱解，而数值相压力几乎在任何时间都强烈地收敛于空间L ^2的弱解。由于相迁移率的简并性和毛细管压力导数的无穷大，证明并不简单。