Leibniz MMS Days 2022 - Abstract

Frerichs-Mihov, Derk

On reducing spurious oscillations in discontinuous Galerkin methods for convection-diffusion equations

Approximating the solution of convection-diffusion equations in the convection-dominated regime by standard methods usually lead on affordable grids to unphysical values, so called spurious oscillations. Standard discontinuous Galerkin methods are known on the one hand to produce sharp layers but on the other hand are also not able to prevent the pollution of the solution. This talk introduces a post-processing method that uses so called slope limiter to automatically detect regions where the solution is polluted and to correct the solution in these regions. Several slope limiting techniques are presented and tested on two standard benchmark problems.