相关论文: On the Stability of IMEX Upwind gSBP Schemes for 1…

We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent…

In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge-Kutta (RK) methods in time and discontinuous Galerkin (DG) methods in space. We…

In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…

We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the…

The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for a class of fourth order gradient flow problems, including…

This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully…

We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…

In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu and T. Xiong, submitted, arxiv:1306.0227] for kinetic transport equations under a…

Recovering some prominent high-order approaches such as the discontinuous Galerkin (DG) or the spectral difference (SD) methods, the flux reconstruction (FR) approach has been adopted by many individuals in the research community and is now…

In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…

Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…

We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…

This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and convection-diffusion problems and the respective transient…

The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…

We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arbitrarily high order approximations in both space and time,…

We propose IMEX HDG-DG schemes for planar and spherical shallow water systems. Of interest is subcritical flow, where the speed of the gravity wave is faster than that of nonlinear advection. In order to simulate these flows efficiently, we…

We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…

We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…