非定常Stokes方程的全离散稳定化有限元格式

A FULLY DISCRETE STABILIZED FINITE ELEMENT FORMULATION FOR NON-STATIONARY STOKES EQUATION

本文研究二维非定常Stokes方程全离散稳定化有限元方法.首先给出关于时间向后一步Euler半离散格式,然后直接从该时间半离散格式出发,构造基于两局部高斯积分的稳定化全离散有限元格式,其中空间用P_1—P_1元逼近,证明有限元解的误差估计.本文的研究方法使得理论证明变得更加简便,也是处理非定常Stokes方程的一种新的途径.

A fully discrete stabilized finite element method is studied for the two-dimensional S- tokes equation. The Euler backward semi-discrete formulation in time for non-stationary Stokes equation is established firstly. And then a fully discrete stabilized finit e element formulation based on two local Gauss integrals for non-stationary Stokes equation is directly established from time semi-discrete formulation. The spatial discretization is based on the P1 - PI triangular element for the approximation of the velocity and pressure. And the error estimates for the fully discrete finite element approximate solutions are derived. The approaches studied here could make theoretical argumentation simper and more convenient. And it is a new pathway for non-stationary equations.