A stabilized Crank-Nicolson mixed finite element method for non-stationary parabolized Navier-Stokes equations

作者：Zhou, Yan-jie; Teng, Fei; Luo, Zhen-dong^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2017, 33(2): 409-416.

DOI：10.1007/s10255-017-0670-5

• parabolized Navier-Stokes equations
• stabilized Crank-Nicolson mixed finite element formulation
• error estimate

In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameterfree with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.

• 出版日期2017-4
• 单位北京工商大学; 华北电力大学; 华北电力大学（保定）