Stokes方程的稳定化间断有限元法

DISCONTINUOUS FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS

本文对定常的Stokes方程提出了一种新的间断有限元法,通过对通常的间断Galerkin有限元法应用稳定化思想,建立了一个相容的稳定间断有限元格式,对速度和压力的任意分片多项式空间Pl(K),Pm(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L2 范数的最优误差估计．

In this paper, we derive a new discontinuous finite element formulation for the Stokes equations, based on the general discontinuous Galerkin methods. This new formulation is stable and consistent for any combination of discrete discontinuous velocity and pressure spaces, when polynomials of degree 1 are used for each component of velocity and polynomials of m for the pressure, for any l ≥ 1 and rn ≥ 0.Optlmal error estimates for the approximation of both velocity and pressure in L^2 norm are obtained for the Stokes problems, as well as an optimal error estimate for the approximation of velocity and pressure in mesh dependent norm.