Abstract

In this talk, we present recent progress on a posteriori error estimation for convection–diffusion equations in the convection-dominated regime. We construct error estimators that scale optimally with respect to both the mesh width and the Peclet number, and are therefore robust in the high-Peclet-number limit. The approach is based on relative entropy stability estimates and a decomposition of the residual into hyperbolic and parabolic components, which allows us to treat transport and dissipation in a unified framework. SIAC filtering is used to recover the necessary regularity at the discrete level.

As a perspective, we plan to use extensions of these estimators to guide adaptive multilevel Monte Carlo approximations of statistical solutions of the barotropic Navier–Stokes equations.

This is joint work with Kiwoong Kwon (Darmstadt) and Sebastian Krumscheid (Karlsruhe).