Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Entropy and efficient numerical schemes for conservation laws

Siddhartha Mishra

ETH Zurich

The entropy inequality has been a very useful design principle for numerical methods approximating hyperbolic systems of conservation laws. We will review the development of entropy stable schemes in the last three decades by highlighting the contributions of Eitan Tadmor in this regard. A new numerical paradigm for the computation of entropy measure valued solutions is also presented and entropy measure valued solutions are demonstrated to be a suitable solution concept for multi-dimensional systems of conservation laws.