Higher-order methods for the Stokes equations based on the coupling of discontinuous Galerkin method and spectral deferred correction method

Abstract

In this paper, the spatial discontinuous Galerkin (DG) approximation coupled with the temporal spectral deferred correction (SDC) evolution for the Stokes equations is adopted to construct the higher-order discretization method. First, the artificial compressibility strategy method is used to convert the Stokes equations into the Cauchy–Kovalevskaja type equations. Second, the corresponding equations can be rewritten as a first-order system by introducing the new variable equal to the gradient of the velocity. Then, the DG and the SDC methods are properly combined to construct the expected higher-order method. Theoretically, the stability analysis of the second-order fully discrete method is proved. The numerical experiments are given to verify the effectiveness of the presented methods.