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.
High order semi-Lagrangian methods and their applications in kinetic simulations and atmospheric modelings.
Dimension reduction methods with high order accuracy for high-dimensional PDEs: sparse grids approach and low-rank tensor approach.
Asymptotic preserving methods for plasma simulations.
Kernel-based methods for efficient time-dependent simulations.