The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow

Abstract

In this paper, we solve the time-dependent Stokes problem by the weak Galerkin (WG) finite element method. Full-discrete WG finite element scheme is obtained by applying the implicit backward Euler method for time discretization. Optimal order error estimates are established for the corresponding numerical approximation in $H^1$ norm for the velocity, and $L^2$ norm for both the velocity and the pressure in semi-discrete forms and full-discrete forms, respectively. Some computational results are presented to demonstrate the accuracy, convergence and efficiency of the method.