An Oseen-Type Post-Processed Finite Element Method Based on a Subgrid Model for the Time-Dependent Navier-Stokes Equations

摘要

An Oseen-type post-processed mixed finite element method based on a subgrid model is presented for the simulation of time-dependent incompressible Navier-Stokes equations. This method first solves a subgrid stabilized nonlinear Navier-Stokes system on a mesh of size H to obtain an approximate solution pair (u(H)(x, T), p(H)(x, T)) at the given final time T, and then post-processes the solution (u(H)(x, T), p(H)(x, T)) by solving a stabilized Oseen problem on a finer mesh or in higher-order finite element spaces. We prove stability of the stabilized method, derive error estimates for the post-processed solutions, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed method.