Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions

• Introduction of dissipative weak solutions for the Euler equations in framework high-order FE methods. First investigation convergence schemes terms equations. Consistency analysis DG methods without any underlying smoothness assumptions. Recipe obtaining a result solutions. Numerical validation using Cesaro averages Kelvin–Helmholtz problem. In this paper, we present finite element based methods, particular, focus on discontinuous Galerkin scheme summation-by-parts operators. To end, it is crucial that structure preserving properties, such as positivity preservation and entropy inequality hold. We demonstrate how to ensure them prove our multidimensional via numerical simulations, verify theoretical results.