Analysis of Multistep Finite Volume Methods for Positive Semidefinite Problem of Two-Phase Incompressible Flow
半正定两相驱动问题的多步有限体积方法及其理论分析

The multidimensional positive semidefinite problem of two-phase incompressible flow in porous media with initial-boundary conditions is considered here. The equations are discretized by multistep upwind finite volume methods on unstructured meshes. It is proved that the error estimates in discrete norms are of order $O(\Delta t^2+h)$, where $\Delta t$ denotes the time step and $h$ denotes the space step. Numerical examples are given at the end to show the efficiency of the method.