Optimal error estimates of the local discontinuous Galerkin method for nonlinear second‐order elliptic problems on Cartesian grids

Mahboub Baccouch

doi:10.1002/num.22538

Optimal error estimates of the local discontinuous Galerkin method for nonlinear second‐order elliptic problems on Cartesian grids

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22538 ◽

2020 ◽

Vol 37 (1) ◽

pp. 505-532

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Optimal Error Estimates ◽

Cartesian Grids ◽

Optimal Error ◽

Local Discontinuous Galerkin ◽

Second Order Elliptic Problems

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Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes

Journal of Scientific Computing ◽

10.1007/s10915-011-9492-4 ◽

2011 ◽

Vol 51 (1) ◽

pp. 1-27 ◽

Cited By ~ 2

Author(s):

Liangyue Ji ◽

Yan Xu

Keyword(s):

Galerkin Method ◽

Surface Diffusion ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Optimal Error Estimates ◽

Optimal Error ◽

Local Discontinuous Galerkin ◽

Cartesian Meshes

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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Optimal Error Estimates of the Discontinuous Galerkin Method with Upwind-Biased Fluxes for 2D Linear Variable Coefficients Hyperbolic Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01197-x ◽

2020 ◽

Vol 83 (1) ◽

Author(s):

Minghui Liu ◽

Boying Wu ◽

Xiong Meng

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Hyperbolic Equations ◽

Variable Coefficients ◽

Optimal Error Estimates ◽

Optimal Error

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Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.01.004 ◽

2018 ◽

Vol 127 ◽

pp. 164-178 ◽

Cited By ~ 10

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Zhihui Liu

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimate ◽

Optimal Error ◽

Local Discontinuous Galerkin

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Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142900371544 ◽

2001 ◽

Vol 39 (1) ◽

pp. 264-285 ◽

Cited By ~ 164

Author(s):

Bernardo Cockburn ◽

Guido Kanschat ◽

Ilaria Perugia ◽

Dominik Schötzau

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Cartesian Grids ◽

Local Discontinuous Galerkin

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Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection–diffusion and KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2006.10.043 ◽

2007 ◽

Vol 196 (37-40) ◽

pp. 3805-3822 ◽

Cited By ~ 55

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Kdv Equations

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Two Efficient and Reliable a posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Linear Elliptic Problems on Cartesian Grids

Journal of Scientific Computing ◽

10.1007/s10915-021-01497-w ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Local Discontinuous Galerkin Method ◽

A Posteriori ◽

A Posteriori Error ◽

Local Discontinuous Galerkin

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A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.08.023 ◽

2014 ◽

Vol 68 (10) ◽

pp. 1250-1278 ◽

Cited By ~ 17

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation

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Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems

Mathematics of Computation ◽

10.1090/s0025-5718-01-01317-5 ◽

2001 ◽

Vol 71 (238) ◽

pp. 455-479 ◽

Cited By ~ 117

Author(s):

Paul Castillo ◽

Bernardo Cockburn ◽

Dominik Schötzau ◽

Christoph Schwab

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Local Discontinuous Galerkin Method ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Priori Error Estimates ◽

Diffusion Problems

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Asymptotically Exact Posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Nonlinear Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-018-0687-9 ◽

2018 ◽

Vol 76 (3) ◽

pp. 1868-1904 ◽

Cited By ~ 1

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Posteriori Error ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Diffusion Problems

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