A parallel partition of unity method for the unsteady Stokes equations

The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems.

This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method.

The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time.

Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.