Numerical solutions of hyperbolic conservation laws and Hamilton-Jacobi equations with high order numerical methods, such as:
Essentially non-oscillatory (ENO) methods and weighted ENO (WENO) finite volume and finite difference methods,
Discontinuous Galerkin (DG) methods,
Model and simulation of the pedestrian flow, magma flow.
Numerical solution of nonlinear wave equations and gradient flows, such as KdV equation, Cahn-Hilliard equation.
Arbitrary Lagrangian-Eulerian methods and computational cosmology.
Efficient time discretization methods.