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

摘要

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 h by choosing a proper coarse mesh size H. However, the two-level method will involve much less work.