相关论文: An Extended Discontinuous Galerkin Method for High…

We study the convergence of the discontinuous Galerkin (DG) method applied to the advection-reaction equation on meshes with reentrant faces. On such meshes, the upwind numerical flux is not smooth, and so the numerical integration of the…

We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate $\Omega$ by a…

The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…

A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed…

The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…

An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…

This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…

We present a non-intrusive model reduction framework for linear poroelasticity problems in heterogeneous porous media using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the…

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using…

We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is…

In [11] and [5], an error estimate of optimal convergence rates and optimal error propagation (optimal^2) was given for the Runge-Kutta discontinuous Galerkin (RKDG) method solving the scalar nonlinear conservation laws in the case of…

We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…

High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations, especially when implemented on GPU-oriented architectures that favor very high polynomial orders. On modern GPUs, high-order polynomial…

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

This work introduces an optimization-based $rp$-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally…

Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal…

We introduce a Lagrangian nodal discontinuous Galerkin (DG) cell-centered hydrodynamics method for solving multi-dimensional hyperbolic systems. By incorporating an adaptation of Zalesak's flux-corrected transport algorithm, we combine a…

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many…

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…