题目: Two-level difference finite element method

主讲人：黄鹏展 教授

时间：2026年09月04日（周五）16:30 —18:00

地点：理学院楼308

主办单位：理学院

主讲人简介:

黄鹏展，新疆大学教授，博士生导师，先后在香港城市大学，美国匹兹堡大学访问。自治区天山创新团队负责人，中国核学会计算物理学会理事。主要从事偏微分方程数值解、计算流体力学的研究。自治区杰出青年科学基金获得者，入选“天山英才”青拔人才。主持国家自然科学基金3项，在IMAJNA、CMAME、CiCP、IJHMT等国际知名期刊上发表SCI论文160余篇。研究成果获自治区自然科学奖一等奖1项等。

摘要：

A difference finite element method based on the mixed finite element pair $((P_1^b,P_1^b,P_1) \times (P_1,P_1,P_1))$-$(P_1 \times P_0)$ is presented for the three-dimensional stationary Navier-Stokes equations with damping.  Moreover, based on this proposed method, a two-level discretization is constructed, which involves solving a problem of the Navier-Stokes equations with damping on coarse mesh with mesh sizes $H$ and $\mathcal{T}$, and a general Stokes problem on fine mesh with mesh sizes $h = O(H^2)$ and $\tau = O(\mathcal{T}^2)$. This two-level difference finite element method provides an approximate solution with the same convergence rate as the difference finite element solution, which involves solving a problem of the Navier-Stokes equations with damping on fine mesh with mesh sizes $h$ and $\tau$. Hence, it can save a large amount of computational time. Finally, all computational results support the theoretical analysis and show the effectiveness of the two-level difference finite element method for solving the considered problem.