This paper presents and analyzes a discontinuous Galerkin method for the incompressible 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.

翻译：本文介绍并分析了一种不连续的 Galerkin 方法, 用于解决多孔介质中无法压缩的三阶段流量问题。 我们使用第一个顺序时间的外推法, 从而可以默认和连续地解答方程式 。 我们显示, 离散的问题已经得到了很好的定位, 并获得了先验的误差估计。 我们的数字结果证实了理论结果, 即算法与第一顺序相融合 。