数学科学研究所
Insitute of Mathematical Science

Applied Mathematics Seminar 18: Difference finite element method for 3D incompressible Navier-Stokes equations

Seminar| Institute of Mathematical Sciences
Time:Friday, December 23rd, 2022, 16:30-17:30
Location:Online, Tencent Meeting
Speaker: Xinlong Feng,  Xinjiang University

AbstractIn 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 inf-sup condition in 2D domain. In addition, we use FE pair ((P1b,P1b,P1)×P1)×(P1×P0) to solve 3D Oseen iterative equations, where the pair satisfies the discrete inf-sup condition in 3D domain. Moreover, we provide the existence and uniqueness of the DFE solutions of 3D Oseen iterative equations and deduce the first order convergence of the DFE solutions to the exact solution of 3D N-S equations. Finally, numerical tests are presented to show the accuracy and effectiveness of the proposed method.

Tencent Meeting Number : 702-6472-0755

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