Pressure Recovery for Weakly Over-Penalized Discontinuous Galerkin Methods for the Stokes Problem

In this paper, two postprocessing procedures for pressure recovery are proposed and analyzed for the weakly over-penalized discontinuous Galerkin methods developed in Liu in SIAM J Numer Anal 49:2165–2181, 2011 for the Stokes problem in two dimensions. These pressure recovery procedures are just elementwise calculations, benefiting from the weak over-penalization in the corresponding velocity schemes. There is no need for solving any discrete linear system in pressure recovery. It is proved that these recovery procedures have optimal order of convergence rates in the L2-norm for the numerical pressure. Three benchmark examples are tested to illustrate the accuracy and efficiency of these procedures.