可压缩可混溶驱动问题的共轭梯度迭代法的误差估计

Error estimate of conjugate gradient iteration method for a model for miscible compressible displacement

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藕合而成 ;压力方程和饱和度方程均是抛物型方程 .对压力方程采用标准有限元方法 ,对饱和度方程用特征 -有限元方法 .对这两个方法离散后所得到的代数方程组 ,利用共轭梯度迭代法求解 .通过详细的理论分析 ,给出了共轭梯度迭代解与原问题真解的最优阶H1

Miscible compressible displacement in a porous media was modelled by a nonlinear coupled system of two parabolic equations: the pressure equation and the concentration equation. The pressure was approximated by a standard Galerkin method while the concentration by a combination of a Galerkin method and the method of characteristics. A conjugate gradient iterative procedure was used to solve the algebraic problems arising from those two approximate schemes. By detailed theoretical analyses, optimal order H 1-error estimates are obtained between the exact solution of original problem and the solution of conjugate gradient iterative procedure.