# Numerical Analysis and Scientific Computing Seminar

## Provably entropy stable subcell finite volume shock capturing for high order spectral element discontinuous Galerkin methods

**Speaker:**
Gregor Gassner, University of Cologne

**Location:**
Warren Weaver Hall online

**Date:**
March 26, 2021, 10 a.m.

**Synopsis:**

In this talk, we explain how to construct a compatible subcell finite volume scheme that can be seemlessly blended with a high order spectral element discontinuous Galerkin method. Our goal applications are the compressible Euler equations and the ideal MHD equations in multiple dimensions. Starting with an entropy-dissipative split-form discontinuous Galerkin scheme on collocated Legendre-Gauss-Lobatto (LGL) nodes, we show how to carefully design a finite volume type discretization on the LGL subcell grid such that it is (i) still provably entropy-dissipative/stable/