许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、 边界层等,其位置随时间而变动. 多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性 的“局部化现象”问题,其数学模型为耦合非线性 偏微分方程组的初边值问题.为减轻数值解在局部前沿位置的数值振荡, 提高解的精确性,本文给出了该 问题 的动态混合元格式和沿特征线修正的动态混合元格式, 证明了其收敛性,并给出了误差估计.

Many time-dependent problems involve localized phenomena, such as sharp fronts, shocks, and layers, which move with time. Miscible displacement problem in porous media is a typical, representative problem with localized phenomena, the models of which can be described as a coupled system of non-linear partial differential equations. To capture this moving local phenomena improve the numerical solution's precision, we present a dynamic mixed finite element we that with its modified form along the characteristic orve for incompressible miscible displacement in porous media, and discuss their convergence and error estimates.