Discontinuous Galerkin methods; Finite element methods
High order methods for MHD, Hamilton-Jacobi, Maxwell's equations in linear and nonlinear media, Vlasov-Maxwell equations, multi-scale kinetic transport models, fluid models
High order structure-preserving methods: divergence-free, well-balanced, energy stable/conservative, positivity preserving, asymptotic preserving
Model order reduction: numerical algorithms and analysis