Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem

Pressure-robustness is an essential demand for the incompressible fluid simulation. In this paper, we develop the enhanced discontinuous Galerkin (DG) finite element methods for solving Stokes equations in the primary velocity-pressure formulation to achieve pressure-robustness. The velocity reconstruction operator has been designed for discontinuous functions and utilized to modify the external source assembling. The new schemes stay almost the same as that in the existing DG schemes but only differ for the source terms. The conforming discontinuous Galerkin and symmetric interior penalty DG have been employed to demonstrate the enhancement. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Several numerical experiments are performed to validate our theoretical conclusions.