Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
This provides an efficient solver for Stokes problems in computational fluid dynamics, though it is an incremental improvement over existing multigrid techniques.
The authors developed a multigrid method for Stokes equations discretized with Hdiv-conforming DG methods, achieving convergence rates independent of mesh size and reasonably small, without needing a Schur complement approximation.
A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and thus does not need a Schur complement approximation. The smoothers used are of overlapping Schwarz type and employ a local Helmholtz decomposition. Additionally, we use the fact that the discretization provides nested divergence free subspaces. We present the convergence analysis and numerical evidence that convergence rates are not only independent of mesh size, but also reasonably small.