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Center for Nonlinear Studies |
High order discontinuous Galerkin (DG) methods combine high order accuracy and geometric flexibility with a computationally convenient structure. However, high order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and under-resolved solution features. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of numerical resolution and solution regularization while retaining formal high order accuracy. In this talk, we will review the construction of robust entropy stable discontinuous Galerkin methods, as well as several extensions including flows on networks and model reduction.
Host: Svetlana Tokareva