不可压渗流驱动问题混合有限元/间断有限元耦合格式的误差分析

摘要

The numerical modeling of the miscible displacement in porous media is important and interesting in the oil recovery field, the environmental pollution problem and so on. A combined approximation is applied in this paper to the given miscible displacement problem including molecular diffusion and dispersion. The mixed finite element method is used for the pressure equation, and the concentration one is solved by the non-symmetric interior penalty discontinuous Galerkin method. Induction hypotheses are used to avoid the inconvenience of the cut-off operator. Based on the properties of the interpolation projection, an a priori hp error estimate is obtained.%多孔介质中渗流驱动问题与环境污染和油藏开采等问题密切相关,是当今的研究热点.对具有分子扩散和弥散效应的不可压渗流驱动问题,本文用混合有限元/间断有限元耦合格式来求解,即用混合有限元方法求解压力方程,用对称内罚间断有限元方法逼近浓度方程.运用比剪切算子更为便捷的归纳假设和插值投影,导出了先验hp误差估计.