A parallel subgrid stabilized finite element method based on fully overlapping domain decomposition for the Navier–Stokes equations

Based on a fully overlapping domain decomposition technique and finite element discretization, a parallel subgrid stabilized method for the incompressible Navier–Stokes equations is proposed and analyzed. In this method, each processor computes a local stabilized solution in its own subdomain by solving a global problem on a mesh that is fine around its own subdomain and coarse elsewhere, where the stabilization term is based on an elliptic operator defined on the same mesh. This method has low communication complexity. It only requires the application of an existing sequential solver on the global meshes associated with each subdomain, and hence can reuse the existing sequential software. Convergence theory of the method is developed. Algorithmic parameter scalings are derived. Numerical results are also given to verify the theoretical predictions and demonstrate the effectiveness of the method.