We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings.
Bibliographical noteFunding Information:
B. Cockburn was supported in part by the National Science Foundation (Grant DMS-0712955) and by the University of Minnesota Supercomputing Institute. G. Kanschat was supported in part by NSF through award no. DMS-0713829 and by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). D. Schötzau was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).
- Discontinuous Galerkin methods
- Equal-order methods
- Incompressible Navier-Stokes equations