A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations
A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations
复制标题
基于欧拉隐式/显式格式的时变纳维-斯托克斯方程罚分有限元法
DOI：
10.1016/j.cam.2010.06.025
复制
发表时间：
2010-12-01
影响因子：
2.4
通讯作者：
Li, Jian
中科院分区：
文献类型：
--
作者：
He, Yinnian;Li, Jian
提出了一种求解二维时变Navier-Stokes方程的全离散罚有限元方法，其中时间离散基于Euler隐/显格式，并包含一些隐式线性项和一个显式非线性项，有限元空间离散基于满足离散inf-sup条件的P（1）b-P-1单元对.这种方法允许我们将速度的计算与压力的计算分开，具有更大的时间步长Δ t，以便容易地计算数值速度u（Δ h）（n）和压力p（Δ h）（n）。当罚参数τ_c、时间步长Δ t和网格尺寸h满足下列稳定性条件时，给出了全离散罚有限元法数值速度和压力的最优误差估计：
A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations, where the time discretization is based on the Euler implicit/explicit scheme with some implicit linear terms and an explicit nonlinear term, and the finite element spatial discretization is based on the P(1)b-P-1 element pair, which satisfies the discrete inf-sup condition. This method allows us to separate the computation of the velocity from the computation of the pressure with a larger time-step size Delta t, so that the numerical velocity u(epsilon h)(n) and the pressure p(epsilon h)(n), are easily computed. An optimal error estimate of the numerical velocity and the pressure is provided for the fully discrete penalty finite element method when the penalty parameter epsilon, the time-step size Delta t and the mesh size h satisfy the following stability conditions: epsilon c(1)