二相驱动问题的一种全离散过程的超收敛性

SUPERCONVERGENCE IN A TIME-DISCRETIZATION PROCEDURE OF MISCIBLE DISPLACEMENT

考虑可混溶不可压缩的二相驱动问题的超收敛性分析，引进一种有效的全离散过程，采用一致网格剖分、指标为ｋ的Ｒａｖｉａｒｔ－Ｔｈｏｍａｓ空间对压力方程作混合有限元逼近；用拟正则剖分、逼近阶为ｌ的全离散Ｇａｌｅｒｋｉｎ方法，其系数中的速度值用具有超收敛性的核函数平均值确定。

An efficient time stepping procedure is introduced to treat the continous time method of Douglas for approximating the solution of the equations describing the miscible displacement of one incompressible fluid by another in porous media.The convergence analysis is a periodic setting.The pressure is approximated by a mixed finite element procedure using a Raviart Thomas space of index k over a uniform grid.The resulting Darcy velocity field is postprocessed by convolution with a Bramble Schatz kernel and this enhanced velocity is used in the evaluation of the coefficients in the Galerkin procedure for the concentration.If the concentration space is of local degree l ,then the error,as measured in L 2 (Ω),in the concentration is 0 (h l+1 c+h 2k+2 p+Δt c+(Δt p) 2) ,which is an optimal reflection of the superconvergent velocity approximation.