中文摘要：

本文考虑裂缝孔隙介质中驱动问题的数值方法及理论分析。我们分别对压力方程采用混合元方法,对裂缝系统上的浓度方程采用特征线交替方向有限元方法,对岩块系统上的浓度方程采用交替方向有限元方法,证明了交替方向有限元格式具有最优L^2-模和H^1-模误差估计。

英文摘要：

The numerical method and theoretical analysis of mathematical model for single phase incompressible flow in naturally fractured reservoirs are considered. The mixed finite element method is adopted to the pressure equation. The alternating direction method combined with the method of characteristic is considered for the saturation equation in the fissures, and alternating direction method is proposed for the saturation equation in the rocks. Optimal error estimates in L^2-norm and H^1-norm are derived for the characteristic-alternating direction finite element method.