Nonstandard Local Discontinuous Galerkin Methods for Fully Nonlinear Second Order Elliptic and Parabolic Equations in High Dimensions

Journal of Scientific Computing ◽

10.1007/s10915-018-0765-z ◽

2018 ◽

Vol 77 (3) ◽

pp. 1534-1565

Author(s):

Xiaobing Feng ◽

Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Galerkin Methods ◽

High Dimensions ◽

Fully Nonlinear ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Elliptic And Parabolic Equations

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Mixed interior penalty discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21856 ◽

2014 ◽

Vol 30 (5) ◽

pp. 1538-1557 ◽

Author(s):

Xiaobing Feng ◽

Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Galerkin Methods ◽

High Dimensions ◽

Interior Penalty ◽

Fully Nonlinear ◽

Elliptic And Parabolic Equations

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Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

Journal of Scientific Computing ◽

10.1007/s10915-013-9763-3 ◽

2013 ◽

Vol 59 (1) ◽

pp. 129-157 ◽

Author(s):

Xiaobing Feng ◽

Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Fully Nonlinear ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Nonlinear Elliptic ◽

Local Discontinuous Galerkin Methods ◽

Elliptic And Parabolic Equations

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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 ◽

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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Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media

Journal of Computational Physics ◽

10.1016/j.jcp.2014.04.009 ◽

2014 ◽

Vol 272 ◽

pp. 88-107 ◽

Author(s):

Ching-Shan Chou ◽

Chi-Wang Shu ◽

Yulong Xing

Keyword(s):

Wave Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Heterogeneous Media ◽

Second Order ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving ◽

Second Order Wave Equation

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Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations

Mathematics of Computation ◽

10.1090/mcom/2975 ◽

2015 ◽

Vol 85 (297) ◽

pp. 63-84 ◽

Author(s):

Waixiang Cao ◽

Zhimin Zhang

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Linear Parabolic Equations

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Fourier Analysis of Local Discontinuous Galerkin Methods for Linear Parabolic Equations on Overlapping Meshes

Journal of Scientific Computing ◽

10.1007/s10915-019-01030-0 ◽

2019 ◽

Vol 81 (2) ◽

pp. 671-688

Author(s):

Nattaporn Chuenjarern ◽

Yang Yang

Keyword(s):

Fourier Analysis ◽

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Linear Parabolic Equations

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Local Discontinuous Galerkin Methods to a Dispersive System of KdV-Type Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01370-2 ◽

2021 ◽

Vol 86 (1) ◽

Author(s):

Chao Zhang ◽

Yan Xu ◽

Yinhua Xia

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Dispersive System ◽

Kdv Type Equations

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Local discontinuous Galerkin methods for the Kuramoto–Sivashinsky equations and the Ito-type coupled KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2005.06.021 ◽

2006 ◽

Vol 195 (25-28) ◽

pp. 3430-3447 ◽

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Kdv Equations ◽

Local Discontinuous Galerkin Methods ◽

Coupled Kdv Equations

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Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2015068 ◽

2016 ◽

Vol 50 (4) ◽

pp. 1083-1105 ◽

Author(s):

Haijin Wang ◽

Shiping Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

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