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 thewetting phase pressure and saturation, which are the primary unknowns. The discrete saturation satisfies a maximum principle. Stability of the scheme and existence of a solution are established.

中文翻译：

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多孔介质中退化两相流的有限元方法。第一部分：适中性

提出了一种质量集总和通量逆向的有限元方法来求解多孔介质中的不混相两相流动问题。该方法直接近似于润湿相压力和饱和度，它们是主要的未知数。离散饱和满足最大值原则。建立了方案的稳定性和解的存在性。