A spacetime discontinuous Galerkin method for the incompressible NavierStokes equations
We introduce a spacetime discontinuous Galerkin (DG) finite element method for the incompressible NavierStokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the methods robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a spacetime hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A spacetime hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 41854204]. We will compare numerical results of the spacetime DG and spacetime HDG methods. This constitutes the first comparison between DG and HDG methods.
spacetime discontinuous galerkin method incompressible navierstokes equations deforming domains