Abstract:
Discontinuous Galerkin (DG) discretizations for the three
parts of the Navier-Stokes equations are discussed. First, we show the
very natural derivation of the DG method by LeSaint and Raviart for
advection problems. Then, the LDG method for the Laplacian and the Stokes
operator is presented. It is combined with the method for advection to
obtain a stable discretization of the Oseen equations. Finally, this
method is applied inside a nonlinear iterative scheme to obtain strongly
divergence free solutions of the incompressible Navier-Stokes equations.
In the second part, the construction of efficient solvers for the discrete
problems is discussed.
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