Related papers: Stable Spectral-Volume Methods
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial…
The flux reconstruction (FR) method has gained popularity within the research community. The approach has been demonstrated to recover high-order methods such as the discontinuous Galerkin (DG) method. Stability analyses have been conducted…
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…
This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop…
We design, analyze and numerically validate a novel discontinuous Galerkin method for solving the coagulation-fragmentation equations. The DG discretization is applied to the conservative form of the model, with flux terms evaluated by…
We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain…
High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This separation hides a simple geometric fact: all three act on…
In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…
In this paper, a shock capturing for high-order entropy stable discontinuous Galerkin spectral element methods on moving meshes is proposed using Gauss--Lobatto nodes. The shock capturing is achieved via the convex blending of the…
The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture…
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low to high order…
We study a class of spatial discretizations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials. In particular, we focus on spectral methods and discontinuous Galerkin approximations. To obtain L 2…
We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…
We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…
We propose an energy-conserving ultra-weak discontinuous Galerkin (DG) method for the generalized Korteweg-De Vries(KdV) equation in one dimension. Optimal a priori error estimate of order $k + 1$ is obtained for the semi-discrete scheme…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…
In this paper, a novel high order semi-Lagrangian (SL) spectral volume (SV) method is proposed and studied for nonlinear Vlasov-Poisson (VP) simulations via operator splitting. The proposed algorithm combines both advantages of…
Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations…