Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

By Bernardo Cockburn, Chi-Wang Shu. Journal of Scientific Computing, 2001

1,922 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ce5ec02de611c5211f8da203b93905f5e2619003

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In Computational Mechanics

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Citations in the corpus

High‐order semi‐implicit time‐integrators for a triangular discontinuous Galerkin oceanic shallow water model (2009, methodology): “Explicit method In order to advance the solution in time while retaining some level of HO accuracy we use thirdorder strong stability preserving (SSP) RK methods (see [32] and [33]).”
A Discontinuous Galerkin Global Shallow Water Model (2005, methodology): “An extensive review of DG methods can be found in Cockburn et al. (2000) and Cockburn and Shu (2001).”
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations (2004, methodology): “In this paper, we develop the locally divergence-free discontinuous Galerkin methods equipped with TVD Runge–Kutta time discretization (RKDG) [8,11,13] for solving two-dimensional Maxwell equations, as our starting point to explore the effective treatment of the divergence-free condition with discon”
ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS (2007, methodology): “For a recent survey on DG methods, we refer the reader to the articles [11, 12, 13 ].”
A high‐order triangular discontinuous Galerkin oceanic shallow water model (2008, methodology): “TIME INTEGRATOR In order to advance the solution in time while retaining some high-order accuracy, we use the strongly stability preserving (SSP) Runge–Kutta third-order (RK3) method of Cockburn and Shu [33].”
Local discontinuous Galerkin methods for nonlinear Schrödinger equations (2005, methodology): “For a detailed description of the method as well as its implementation and applications, we refer the readers to the lecture notes [7], the survey paper [9], other papers in that Springer volume, and the review paper [14].”
Stability in the almost everywhere sense: A linear transfer operator approach (2010, methodology): “Several techniques [19,20] have been developed to solve these equations in 2 and 3 dimensions.”
THE DIRECT DISCONTINUOUS GALERKIN (DDG) METHOD FOR DIFFUSION WITH INTERFACE CORRECTIONS (2010, methodology): “Liu’s research was partially supported by the National Science Foundation under the Kinetic FRG Grant DMS07-57227.”
L2 Stability Analysis of the Central Discontinuous Galerkin Method and a Comparison between the Central and Regular Discontinuous Galerkin Methods (2008, methodology): “[2,4]).”
On a One-Sided Post-Processing Technique for the Discontinuous Galerkin Methods (2003, methodology): “The details of the discontinuous Galerkin method that we will be using can be found in [9, 8, 5, 4, 10, 3, 12].”
The embedded discontinuous Galerkin method: application to linear shell problems (2007, methodology): “From the late 1980s to the late 1990s, the method was extended to nonlinear hyperbolic equations, mostly modelling fluid dynamics problems, see the review [2].”