高次有限体积法构造，理论分析及其应用

本项目研究最优高次有限体积法的构造，分析和应用。我们将主要探讨2维和3维具有最优收敛阶的高次有限体积格式的构造和误差分析理论，并将这些有限体积格式应用于多孔介质多相流和Monege-Ampere方程的快速数值模拟。

In this project, we will investigate the construction, analysis and applications of the optimal high-order finite volume schemes. We will first study the construction and error analysis of the 2D and 3D optimal high-order finite volumes schemes, and then apply these schemes to simulate the multi-phase flow in the porous media and to solve numerically the fully nonlinear Monge-Ampere equation.