可压溶混流的混合元逼近

MIXED FINITE ELEMENT APPROXIMATIONS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT

二维和三维空间中，多孔介质里可压溶混流被非线性偏微分方程组所描述．浓度方程采用Galerkin方法逼近，而压力方程采用混合有限元逼近．我们导出了浓度、压力、速度及其时间导数的最优L2误差估计，同时得到了浓度和压力的拟最优L∞误差估计．本文处理了带分子弥散的非线性问题．

A nonlinear partial differential system describing compressible displacement inporous media in R2 or R3 is given. The concentration equation is treated by Galerkin methodand the pressure equation is treated by a parabolic mixed finite element method. Optimalorder error estimates on the concentration, pressure and velocity, and their time derivativesin L2, and almost optimal-order error estimates on the concentration and pressure in L∞ areobtained. One contribution of this paper is the demonstration of how molecular dispersion canbe handled.