Numerical solutions of conservation laws and in general convection dominated problems using:
Essentially non-oscillatory (ENO) methods and weighted ENO (WENO) methods
Discontinuous Galerkin (DG) methods
Numerical solutions of nonlinear wave equations using local discontinuous Galerkin (LDG) methods
Numerical solutions of MHD equations using DG methods
Numerical solutions of water wave equations with free-surface using space-time discontinuous Galerkin (STDG) methods
Numerical solutions of incompressible Navier-Stokes equations using DG methods
Discontinuous Hamiltonian Finite Element Method for Bilinear Poisson Brackets
Numerical solutions of gradient flows using LDG methods
Accuracy-enhancement technique of discontinuous Galerkin solutions
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