Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations

Waixiang Cao; Chi-Wang Shu; Yang Yang; Zhimin Zhang

doi:10.1137/140996203

Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/140996203 ◽

2015 ◽

Vol 53 (4) ◽

pp. 1651-1671 ◽

Cited By ~ 32

Author(s):

Waixiang Cao ◽

Chi-Wang Shu ◽

Yang Yang ◽

Zhimin Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Two Dimensional

Download Full-text

Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction

Communications in Computational Physics ◽

10.4208/cicp.oa-2020-0226 ◽

2021 ◽

Vol 30 (4) ◽

pp. 1150-1184

Author(s):

global sci

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Two Dimensional ◽

Dirac Equations ◽

Nonlinear Dirac Equations

Download Full-text

An Energy Stable Approach for Discretizing Hyperbolic Equations with Nonconforming Discontinuous Galerkin Methods

Journal of Scientific Computing ◽

10.1007/s10915-018-0682-1 ◽

2018 ◽

Vol 76 (3) ◽

pp. 1742-1784 ◽

Cited By ~ 3

Author(s):

Jeremy E. Kozdon ◽

Lucas C. Wilcox

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Energy Stable

Download Full-text

Stabilized discontinuous Galerkin methods for scalar linear hyperbolic equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.05.047 ◽

2006 ◽

Vol 182 (2) ◽

pp. 1623-1628

Author(s):

Mi-Young Kim

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Linear Hyperbolic Equations

Download Full-text

Entropy stable spacetime discontinuous Galerkin methods for the two-dimensional compressible Navier–Stokes equations

Communications in Mathematical Sciences ◽

10.4310/cms.2018.v16.n8.a3 ◽

2018 ◽

Vol 16 (8) ◽

pp. 2095-2124

Author(s):

Andreas Hiltebrand ◽

Sandra May

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Stokes Equations ◽

Navier Stokes ◽

Galerkin Methods ◽

Two Dimensional ◽

Navier Stokes Equations ◽

Entropy Stable

Download Full-text

Superconvergence of Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/18m122916x ◽

2019 ◽

Vol 57 (5) ◽

pp. 2142-2165 ◽

Cited By ~ 2

Author(s):

Qi Tao ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Arbitrary Lagrangian Eulerian ◽

Linear Hyperbolic Equations

Download Full-text

Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations

Journal of Computational Mathematics ◽

10.4208/jcm.2002-m2019-0305 ◽

2021 ◽

Vol 39 (4) ◽

pp. 629-648

Author(s):

global sci

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Degree Polynomial ◽

Optimal Convergence ◽

Polynomial Approximations ◽

Linear Hyperbolic Equations

Download Full-text

Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2005.06.007 ◽

2005 ◽

Vol 208 (1-2) ◽

pp. 21-58 ◽

Cited By ~ 51

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Nonlinear Wave ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Nonlinear Wave Equations ◽

Galerkin Methods ◽

Two Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

Download Full-text

Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/130946873 ◽

2014 ◽

Vol 52 (5) ◽

pp. 2555-2573 ◽

Cited By ~ 34

Author(s):

Waixiang Cao ◽

Zhimin Zhang ◽

Qingsong Zou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Linear Hyperbolic Equations

Download Full-text

Multilevel Preconditioning of Two-dimensional Elliptic Problems Discretized by a Class of Discontinuous Galerkin Methods

SIAM Journal on Scientific Computing ◽

10.1137/060667372 ◽

2008 ◽

Vol 30 (2) ◽

pp. 684-706 ◽

Cited By ~ 7

Author(s):

Johannes K. Kraus ◽

Satyendra K. Tomar

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Galerkin Methods ◽

Two Dimensional ◽

Multilevel Preconditioning

Download Full-text

Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results

Applied Numerical Mathematics ◽

10.1016/j.apnum.2006.07.027 ◽

2007 ◽

Vol 57 (5-7) ◽

pp. 629-645 ◽

Cited By ~ 15

Author(s):

Yunxian Liu ◽

Chi-Wang Shu

Keyword(s):

Performance Assessment ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Two Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Moment Models

Download Full-text