Discontinuous Galerkin Methods for Elliptic Problems

By Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, Donatella Marini. 2000

284 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8ee2efe87fa90dff7f1fb1b72625e3eeeb5bd062

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems (2003, methodology): “For a nice survey of various discontinuous Galerkin methods, see [3].”
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems (2000, methodology): “Rivi ere, Wheeler and Girault 35] and Rivi ere and Wheeler 34] analyzed several variations of the DG method of Baumann and Oden (involving interior penalty techniques) as applied to non-linear convectiondiiusion problems and, nally, S uli, Schwab and Houston 38] synthesized the selfadjoint elliptic,”
Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier–Stokes equations (2002, background): “The aim of this paper is to present a critical comparison between two of the previously mentioned methods, namely that introduced by the authors, see e.g. References [2; 3] and the method of Baumann and Oden described in References [5; 6].”
On 2D elliptic discontinuous Galerkin methods (2006, methodology): “In this paper we expand on previous expositions [3, 4, 5] by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the DG method.”
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems (2001, methodology): “[11] who established a unified framework to study and compare the LDG method and almost all other DG methods for elliptic problems.”
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems (2001, methodology): “In [2], we showed how to choose these numerical fluxes to recover virtually all the DG methods that have been proposed so far; see Table 3.”
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes (2016, unknown): “…approximation spaces in the context of (cid:12)nite element methods also 2 TITLE WILL BE SET BY THE PUBLISHER (cid:12)rst appeared around the same time [12,13]; for reviews of some of the main developments in the subject, we refer to the monographs [27,28] and the articles [8,24].”
Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k–ω turbulence model equations (2005, methodology): “This DG method was first introduced in [12] for the discretization of the viscous terms of the Navier–Stokes equations, and, following the naming convention subsequently introduced in [3], will be called ‘‘BR1 scheme’’.”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, unknown): “On the other hand, the non-symmetric Nitsche method leads to unsymmetric system matrices, convergence is currently only proved for basis functions of degree p ≥ 2, and convergence rates of the L(2) error are suboptimal [3, 4, 46, 58, 59].”
Optimal BV estimates for a discontinuous Galerkin method for linear elasticity (2004, methodology): “In the case of the scalar Poisson equation [2, 3, 7, 8, 9, 18, 22], there is no need to distinguish between the norms (2.”