$L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations

Yingda Cheng; Ching-Shan Chou; Fengyan Li; Yulong Xing

doi:10.1090/mcom/3090

$L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations

Mathematics of Computation ◽

10.1090/mcom/3090 ◽

2016 ◽

Vol 86 (303) ◽

pp. 121-155 ◽

Cited By ~ 12

Author(s):

Yingda Cheng ◽

Ching-Shan Chou ◽

Fengyan Li ◽

Yulong Xing

Keyword(s):

Discontinuous Galerkin ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional

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Optimal error estimates of discontinuous Galerkin methods with generalized fluxes for wave equations on unstructured meshes

Mathematics of Computation ◽

10.1090/mcom/3605 ◽

2020 ◽

pp. 1

Author(s):

Zheng Sun ◽

Yulong Xing

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Unstructured Meshes ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error

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The hp- and h-versions of the discontinuous and local discontinuous Galerkin methods for one-dimensional singularly perturbed models

Applied Numerical Mathematics ◽

10.1016/j.apnum.2011.08.001 ◽

2011 ◽

Vol 61 (12) ◽

pp. 1223-1236 ◽

Cited By ~ 2

Author(s):

Kassem Mustapha

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Well-posedness of hp-version discontinuous Galerkin methods for fractional diffusion wave equations

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drt048 ◽

2013 ◽

Vol 34 (4) ◽

pp. 1426-1446 ◽

Cited By ~ 51

Author(s):

K. Mustapha ◽

D. Schotzau

Keyword(s):

Discontinuous Galerkin ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Well Posedness ◽

Galerkin Methods ◽

Diffusion Wave

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Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results

Electrical Performance of Electronic Packaging IWCE-04 ◽

10.1109/iwce.2004.1407380 ◽

2004 ◽

Author(s):

Yunxian Liu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Moment Models

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Superconvergence of local discontinuous Galerkin methods for one-dimensional convection–diffusion equations

Computers & Structures ◽

10.1016/j.compstruc.2008.11.012 ◽

2009 ◽

Vol 87 (11-12) ◽

pp. 630-641 ◽

Cited By ~ 20

Author(s):

Yingda Cheng ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

One Dimensional ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Numerical resolution of discontinuous Galerkin methods for time dependent wave equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2011.05.010 ◽

2011 ◽

Vol 200 (41-44) ◽

pp. 2814-2827 ◽

Cited By ~ 18

Author(s):

Xinghui Zhong ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Time Dependent ◽

Galerkin Methods ◽

Numerical Resolution

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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

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One-Dimensional Shock-Capturing for High-Order Discontinuous Galerkin Methods

ECCOMAS Multidisciplinary Jubilee Symposium ◽

10.1007/978-1-4020-9231-2_21 ◽

2008 ◽

pp. 307-325 ◽

Cited By ~ 2

Author(s):

E. Casoni ◽

J. Peraire ◽

A. Huerta

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Shock Capturing ◽

Galerkin Methods ◽

One Dimensional

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Mixed Interior Penalty Discontinuous Galerkin Methods for One-Dimensional Fully Nonlinear Second Order Elliptic and Parabolic Equations

Journal of Computational Mathematics ◽

10.4208/jcm.1401-m4357 ◽

2014 ◽

Vol 32 (2) ◽

pp. 107-135 ◽

Cited By ~ 1

Author(s):

Xiaobing Feng and Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Galerkin Methods ◽

Interior Penalty ◽

Fully Nonlinear ◽

One Dimensional ◽

Elliptic And Parabolic Equations

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One-dimensional shock-capturing for high-order discontinuous Galerkin methods

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.3682 ◽

2012 ◽

Vol 71 (6) ◽

pp. 737-755 ◽

Cited By ~ 16

Author(s):

E. Casoni ◽

J. Peraire ◽

A. Huerta

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Shock Capturing ◽

Galerkin Methods ◽

One Dimensional

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