An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110294 ◽

2021 ◽

pp. 110294

Author(s):

Wei Guo ◽

Juntao Huang ◽

Zhanjing Tao ◽

Yingda Cheng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Sparse Grid ◽

High Dimensions ◽

Local Discontinuous Galerkin ◽

Jacobi Equations

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A local discontinuous Galerkin method for directly solving Hamilton–Jacobi equations

Journal of Computational Physics ◽

10.1016/j.jcp.2010.09.022 ◽

2011 ◽

Vol 230 (1) ◽

pp. 232-244 ◽

Author(s):

Jue Yan ◽

Stanley Osher

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin ◽

Jacobi Equations

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An Arbitrary Lagrangian–Eulerian Local Discontinuous Galerkin Method for Hamilton–Jacobi Equations

Journal of Scientific Computing ◽

10.1007/s10915-017-0471-2 ◽

2017 ◽

Vol 73 (2-3) ◽

pp. 906-942 ◽

Author(s):

Christian Klingenberg ◽

Gero Schnücke ◽

Yinhua Xia

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Arbitrary Lagrangian Eulerian ◽

Local Discontinuous Galerkin ◽

Jacobi Equations

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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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Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.02.003 ◽

2021 ◽

Vol 165 ◽

pp. 22-34

Author(s):

Hamid Safdari ◽

Majid Rajabzadeh ◽

Moein Khalighi

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Local Discontinuous Galerkin ◽

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Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7077 ◽

2020 ◽

Author(s):

Hadi Mohammadi‐Firouzjaei ◽

Hojatollah Adibi ◽

Mehdi Dehghan

Keyword(s):

Wave Equation ◽

Laplace Transform ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Wave ◽

Local Discontinuous Galerkin ◽

Distributed Order

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A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2013.866233 ◽

2014 ◽

Vol 91 (9) ◽

pp. 2021-2038 ◽

Author(s):

Xindong Zhang ◽

Yinnian He ◽

Leilei Wei ◽

Bo Tang ◽

Shaoli Wang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

One Dimensional ◽

Fisher’S Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fisher's Equation

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Simulation study of planar and nonplanar super rogue waves in an electronegative plasma: Local discontinuous Galerkin method

Physics of Plasmas ◽

10.1063/1.4983327 ◽

2017 ◽

Vol 24 (5) ◽

pp. 052118 ◽

Author(s):

S. A. El-Tantawy ◽

Tarek Aboelenen

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Simulation Study ◽

Local Discontinuous Galerkin Method ◽

Rogue Waves ◽

Local Discontinuous Galerkin ◽

Electronegative Plasma

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Local discontinuous Galerkin method for solving Burgers and coupled Burgers equations

Chinese Physics B ◽

10.1088/1674-1056/20/11/110205 ◽

2011 ◽

Vol 20 (11) ◽

pp. 110205 ◽

Author(s):

Rong-Pei Zhang ◽

Xi-Jun Yu ◽

Guo-Zhong Zhao

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Burgers Equations ◽

Local Discontinuous Galerkin

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Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21756 ◽

2012 ◽

Vol 29 (5) ◽

pp. 1441-1458 ◽

Author(s):

Leilei Wei ◽

Yinnian He ◽

Bo Tang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Kawahara Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin

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An a priori error estimate for the local discontinuous Galerkin method applied to two-dimensional shallow water and morphodynamic flow

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21914 ◽

2014 ◽

Vol 31 (2) ◽

pp. 397-421 ◽

Author(s):

Chris Mirabito ◽

Clint Dawson ◽

Vadym Aizinger

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Shallow Water ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Local Discontinuous Galerkin Method ◽

Two Dimensional ◽

A Priori Error Estimate ◽

Local Discontinuous Galerkin

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