Abstract

We introduce the concept of dissipative solutions to the compressible Euler system and discuss its basic properties: Weak-weak uniqueness, stability, maximal energy dissipation - entropy production. Then we show that dissipative solutions form a perfect target object for energy dissipating numerical schemes. Introducing the concept of K-convergence (Komlós convergence) we show that Cesàro averages of numerical solutions approach strongly (a.e. pointwise) to a dissipative solution of the Euler system.