Dominik Schoetzau
Department of Mathematics
University of British Columbia
We present and analyze exactly divergence-free discontinuous Galerkin finite element methods for the discretization of linear convection-diffusion problems. The main advantages of these methods in comparison with standard conforming finite element approaches lie in their robustness in transport-dominated regimes, their local conservation properties, their flexibility in the mesh-design, and their exact satisfaction of the incompressibility constraint. We derive the methods for the incompressible Navier-Stokes equations, discuss their stability properties and carry out their numerical analysis. We also present numerical results that confirm the theoretical results and highlight the advantages of these methods.