Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent
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A unified study is presented in this paper for the design and analysis of different finite
element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs …

Based on a novel numerical flux involving jumps of even order derivatives of the numerical
solution, a direct discontinuous Galerkin (DDG) method for diffusion problems was …

We consider a class of time-dependent second order partial differential equations governed
by a decaying entropy. The solution usually corresponds to a density distribution, hence …

A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in
combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for …

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods
[8],[9],[19],[21] for convection diffusion equations on unstructured triangular mesh. We …

Abstract A Direct Discontinuous Galerkin (DDG) method is developed for solving the
compressible Navier–Stokes equations on arbitrary grids in the framework of DG methods …

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-
dependent Maxwellʼs equations when metamaterials are involved. Both semi-and fully …

In this paper, we design high-order bound-preserving discontinuous Galerkin (DG) methods
for multicomponent chemically reacting flows. In this problem, the density and pressure are …

We study a class of degenerate convection–diffusion equations with a fractional non-linear
diffusion term. This class is a new, but natural, generalization of local degenerate convection …