
Numerical solutions of hyperbolic conservation laws and HamiltonJacobi equations with high order numerical methods, such as:
Essentially nonoscillatory (ENO) methods and weighted ENO (WENO) finite volume and finite difference methods,
Discontinuous Galerkin (DG) methods,
Spectral methods.
Model and simulation of the pedestrian flow, magma flow.
Numerical solution of nonlinear wave equations and gradient flows, such as KdV equation, CahnHilliard equation.
Arbitrary LagrangianEulerian methods and computational cosmology.
Efficient time discretization methods.