不可压混溶驱替问题的流线扩散──混合元数值模拟

A MIXED FINITE ELEMENT METHOD COMBINED WITH STREAMLINE DIFFUSION METHOD FOR THE INCOMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

采用标准元模拟不可压混溶流问题，当扩散系数矩阵小过剖分参数时，有限元格式仅能给出比最优精度低一阶的逼近解，格式稳定性差并伴有强烈的数值弥散现象．为了克服上述缺陷，本文对压力方程采用混合元，而对浓度方程采用流线扩散格式，在扩散矩阵为线性的假定下，证明了该格式具有较标准元更高的逼近精度（比最优阶低1／2）和更好的稳定性．

Using the standard finite element to model the incompressible miscible displacement, one can only get the error estimates one order lower than the optimal and onlyget an unstable scheme when the diffusion coefficient matrix is smaller than the triangulationparameter.To overcome these defects of the standard method, in this paper, we present a new finiteelement procedure, which approximates the pressure by a mixed finite element and the concentration by a streamline diffusion method. Under the assumption that the diffusion matrix islinear and is smaller than the triangulation parameter, we prove that the scheme is of bettererror accuracy and stronger stability than the standard finite element discussed before.