Weak Galerkin Finite Element Method for the Unsteady Stokes Equation

摘要

The Weak Galerkin (WG) finite element method for the unsteady Stokes equations in the primary velocity-pressure formulation is introduced in this paper. Optimal-order error estimates are established for the corresponding numerical approximation in an >> style="font-family:;" "=""> style="font-family:Verdana;"> style="font-family:Verdana;">H style="font-family:Verdana;">1 style="font-family:Verdana;"> style="font-family:Verdana;"> style="font-family:Verdana;"> norm for the velocity, and >> style="font-family:;" "=""> style="font-family:Verdana;"> style="font-family:Verdana;">L style="font-family:Verdana;">2 style="font-family:Verdana;"> style="font-family:Verdana;"> style="font-family:Verdana;"> norm for both the velocity and the pressure by us style="font-family:Verdana;"> style="font-family:Verdana;"> style="font-family:Verdana;">e of style="font-family:Verdana;"> style="font-family:Verdana;"> style="font-family:Verdana;"> the Stokes projection.