A two-level finite element method for the Navier-Stokes equations based on a new projection

作者：Liu, Qingfang; Hou, Yanren^*

来源：Applied Mathematical Modelling, 2010, 34(2): 383-399.

DOI：10.1016/j.apm.2009.04.019

• Two-level method
• Finite element method
• Navier-Stokes equations
• Crank-Nicolson scheme
• A new projection

We consider a fully discrete two-level approximation for the time-dependent Navier-Stokes equations in two dimension based on a time-dependent projection. By defining this new projection, the iteration between large and small eddy components can be reflected by its associated space splitting. Hence, we can get a weakly coupled system of large and small eddy components. This two-level method applies the finite element method in space and Crank-Nicolson scheme in time. Moreover,the analysis and some numerical examples are shown that the proposed two-level scheme can reach the same accuracy as the classical one-level Crank-Nicolson method with a very fine mesh size It by choosing a proper coarse mesh size H. However, the two-level method will involve much less work.

• 出版日期2010-2
• 单位西安交通大学