Related papers: Superconvergence Extraction of Upwind Discontinuou…
Higher-order accuracy (order of $k+1$ in the $L^2$ norm) is one of the well known beneficial properties of the discontinuous Galerkin (DG) method. Furthermore, many studies have demonstrated the superconvergence property (order of $2k+1$ in…
In this paper we investigate the superconvergence properties of the discontinuous Galerkin method based on the upwind-biased flux for linear time-dependent hyperbolic equations. We prove that for even-degree polynomials, the method is…
In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove, for any polynomial degree $k$, the $2k+1$th (or $2k+1/2$th)…
This article establishes the usefulness of the Smoothness-Increasing Accuracy-Increasing (SIAC) filter for reducing the errors in the mean and variance for a wave equation with uncertain coefficients solved via generalized polynomial chaos…
This article considers the application of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering for the non-linear stabilization of discontinuous Galerkin (DG) discretizations via entropy correction. Upon constructing discrete filters…
We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly…
In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…
We analyze the superconvergence properties of ultra-weak discontinuous Galerkin (UWDG) methods with various choices of flux parameters for one-dimensional linear Schr\"odinger equation. In our previous work [10], stability and optimal…
Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the…
Linear wave equations sourced by a Dirac delta distribution $\delta(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with…
The Discontinuous Galerkin (DG) method applied to hyperbolic differential equations outputs weakly-linked polynomial pieces. Post-processing these pieces by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution with B-splines can…
In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order…
We present a hybrid filter that is only applied to the approximation at the final time and allows for reducing errors away from a shock as well as near a shock. It is designed for discontinuous Galerkin approximations to PDEs and combines a…
In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We prove, for any polynomial degree $k$, that the numerical…
This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs…
Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods…
In this paper, we concentrate on the superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional linear time-dependent fourth-order equations. The adjustable numerical viscosity of the…
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…
The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…