Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent
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We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …

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 …

The discontinuous Galerkin methods are locally conservative, high‐order accurate, and
robust methods that can easily handle elements of arbitrary shapes, irregular triangulations …

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

We consider an optimization-based limiter for enforcing positivity of internal energy in a semi-
implicit scheme for solving gas dynamics equations. With Strang splitting, the compressible …

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 …

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for
solving time-dependent Poisson–Nernst–Planck systems. Both the semi-discrete and fully …

This paper is concerned with the application of k-exact finite volume methods for
compressible Reynolds-Averaged Navier-Stokes computations of flows around aeronautical …

In this paper, we present the optimal $ L^ 2$-error estimate of $ O (h^{k+ 1}) $ for polynomial
elements of degree $ k $ of the semidiscrete direct discontinuous Galerkin method for …