Error Estimates of EDG-HDG Methods for the Stokes Equations with Dirac Measures

In this paper, we analyze the hybridized, embedded-hybridized and embedded discontinuous Galerkin methods for the Stokes equations with Dirac measures. The velocity, the velocity traces and the pressure traces are approximated by polynomials of degree k >= 1, and the pressure is discretized by polynomials of degree k - 1. An attractive property, named divergence-free, is satisfied by the discrete velocity field. Moreover, the discrete velocity fields derived by hybridized and embedded-hybridized discontinuous Galerkin methods are H(div)-conforming. Using duality argument and Oswald interpolation, a priori and a posteriori error estimates are obtained for the velocity in L-2-norm. In addition, a posteriori error estimates for the velocity in W-1,W-q-seminorm and the pressure in L-q-norm are also derived. Finally, numerical examples are provided to validate the theoretical analysis and show the performance of the obtained a posteriori error estimators.