多孔介质中可压缩可混溶驱动问题的特征—有限体积元法H^1模误差估计

H^1-norm error estimates of the Characteristics-Finite Volume Element method for compressible miscible displacement in porous media

有界区域上多孔介质中可压缩可混溶驱动问题由两个非线性抛物型方程耦合而成:压力方程和饱和度方程均是抛物型方程.对压力方程采用有限体积元法,对饱和度方程采用特征—有限体积元法进行数值分析.给出了全离散特征—有限体积元格式,并通过详细的理论分析,得到了近似解与原问题真解的最优H1模误差估计.

Miscible compressible displacement in a porous media is modelled by a nonlinear coupled system of two parabolic equations： the pressure equation and the concentration equation. Finite volume element method is used for the first equation, and the second concentration equation is treated by a combination of the finite volume element method and the method of characteristics. By detailed theoretical analyses, optimal order in H^1 -error estimates is obtained between the exact solution of original problem and the solution of these fully discrete schemes.