报告题目 (Title)：Difference finite element method for 3D incompressible N-S equations

报告人 (Speaker)：冯新龙 教授（新疆大学）

报告时间 (Time)：2023年8月27日 (周日) 10:30

报告地点 (Place)：校本部E421

邀请人(Inviter)：刘见礼

主办部门：理学院数学系

摘要： In this work, a difference finite element (DFE) method is presented for 3D incompressible Navier-Stokes(N-S) equations. This new method consists of transmitting the FE solution of 3D steady N-S equations into a series of the FE solution of 2D steady Oseen iterative equations, which are solved by using the FE pair (P1b,P1b,P1)×P1 satisfying the discrete LBB condition in 2D domain. Moreover, we use FE pair ((P1b,P1b,P1)×P1)×(P1×P0) to solve 3D Oseen iterative equations, where the pair satisfies the discrete LBB condition in 3D domain. Next, we provide the existence and uniqueness of the DFE solutions of 3D Oseen iterative equations and deduce the convergence of the DFE solutions to the exact solution of 3D problems. Finally, numerical examples are presented to show the accuracy and effectiveness.