An incompressible miscible displacement problem is investigated. A two-grid algorithm of a full-discretized combined mixed finite element and discontinuous Galerkin approximation to the miscible displacement in porous media is proposed. The error estimate for the concentration in \(H^1\)-norm and the error estimates for the pressure and the velocity in \(L^2\)-norm are obtained. The analysis shows that the asymptotically optimal approximation can be achieved as long as the mesh size satisfies \(h = O(H^2)\), where H and h are the sizes of the coarse mesh and the fine mesh, respectively. Meanwhile, the effectiveness of the presented algorithm is verified by numerical experiments, from which it can be seen that the algorithm is spent much less time.

研究了一个不可压缩的混相位移问题。提出了多孔介质混相位移的全离散组合混合有限元和非连续伽辽金近似的双网格算法。获得了\(H^1\) -范数中浓度的误差估计以及\(L^2\) -范数中压力和速度的误差估计。分析表明，只要网格尺寸满足\(h = O(H^2)\)，就可以实现渐近最优逼近，其中H和h分别是粗网格和细网格的大小。同时，通过数值实验验证了所提出算法的有效性，可以看出该算法花费的时间要少得多。