定常Navier-Stokes方程的三个梯度-散度稳定化Taylor-Hood有限元

Three Grad-Div stabilized Taylor-Hood finite elements for steady Navier-Stokes eqution

本文针对定常Navier-Stokes方程给出了三种梯度-散度稳定化Taylor-Hood元.为了克服Taylor-Hood混合有限元离散迭代解不满足质量守恒律的问题,本文在已有的三种迭代格式上增加了梯度-散度稳定项,以便在得到连续离散速度和压力解的同时使离散速度解满足质量守恒律.在强唯一性条件下,本文证明了这三种梯度-散度稳定化Taylor-Hood元迭代格式的离散解在一定迭代次数下逼近Scott-Vogelius混合有限元离散解.数值实验验证了本文的结果.

We propose three Grad-Div stabilized Taylor-Hood finite elements for steady Navier-Stokes equation.To avoid the of the solutions obtained with Taylor-Hood finite elements problem of,a grad-div stabilized term is added to the iterative formats proposed by He,et al,such that we can get continuous velocity and pressure,as well as the velocity solutions obeying mass conservation.Under the strong uniqueness conditionss we show that the grad-div stabilized Taylor-Hood finite element iterative solutions converge to Scott-Vogelius solutions.Finally,numerical examples verify the efficiency of the finite elements.