Discontinuous Galerkin (DG) Finite Element Method for the Improved Stokes Equations

Abstract

In this paper, firstly, discontinuous Galerkin method for improved Stokes equation is proposed. We derive a discontinuous Galerkin (DG) finite element formulation for the improved Stokes equations. Special case of the generalized solution equation for linear and stationary improved Stokes equations retrogresses into generalized solution equation for classical Stokes equation. It is proved that the classical solution and the generalized solution is consistent for the improved Stokes equations, existence and uniqueness of generalized solution for the improved Stokes equations are also proved.