Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the...