In this survey article, we will give a short summary of the basic algorithm issues of
discontinuous Galerkin methods for time-dependent convection dominated problems. We …

Cavitation effects play a substantial role in the dynamic response of marine structures. In the
previous numerical studies, it's assumed that the incident explosive loading is reflected by …

We analyze discontinuous Galerkin methods using upwind-biased numerical fluxes for time-
dependent linear conservation laws. In one dimension, optimal a priori error estimates of …

Solving wave propagation problems within heterogeneous media has been of great interest
and has a wide range of applications in physics and engineering. The design of numerical …

The shock wave and cavitation are main effects in the far-field underwater explosion, which
could cause serious damage to marine structures. In this paper, the fluid mechanical …

We devise the first symplectic Hamiltonian hybridizable discontinuous Galerkin (HDG)
methods for the acoustic wave equation. We discretize in space by using a Hamiltonian …

Simulation of electromagnetic wave propagation in metamaterials leads to more
complicated time domain Maxwell's equations than the standard Maxwell's equations in free …

In this paper, we present a fully discrete scheme by discretizing the space with the local
discontinuous Galerkin method and the time with the Crank–Nicholson scheme to simulate …

Sparse-grid methods have recently gained interest in reducing the computational cost of
solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid …

This paper studies a local discontinuous Galerkin method combined with fourth order
exponential time differencing Runge-Kutta time discretization and a fourth order …