High order numerical methods for hyperbolic conservation laws and Hamilton-Jacobi equations:
– High order spatial discretization: discontinuous Galerkin finite element methods, finite difference/volume WENO methods, etc.
– High order temporal discretization: Runge-Kutta methods, Lax-Wendroff type methods, integral defer correction methods, etc.
Sparse grid methods for high-dimensional PDEs.
Asymptotic preserving methods for plasma simulations.
Method of lines transpose approaches for efficient transport simulations.
High order semi-Lagrangian methods and their applications in kinetic simulations and atmospheric modelings.