An adaptive high-order discontinuous Galerkin method with error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case

Journal of Computational Physics ◽

10.1016/j.jcp.2007.05.003 ◽

2007 ◽

Vol 226 (1) ◽

pp. 1027-1058 ◽

Author(s):

Yanlai Chen ◽

Bernardo Cockburn

Keyword(s):

Steady State ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Error Control ◽

One Dimensional ◽

The One ◽

Jacobi Equations ◽

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An adaptive method with rigorous error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case

Applied Numerical Mathematics ◽

10.1016/j.apnum.2004.08.030 ◽

2005 ◽

Vol 52 (2-3) ◽

pp. 175-195 ◽

Author(s):

Bernardo Cockburn ◽

Bayram Yenikaya

Keyword(s):

Steady State ◽

Error Control ◽

Adaptive Method ◽

One Dimensional ◽

The One ◽

Rigorous Error ◽

Jacobi Equations ◽

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A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

Journal of Computational Physics ◽

10.1016/j.jcp.2018.02.012 ◽

2018 ◽

Vol 362 ◽

pp. 95-113 ◽

Author(s):

Jian Cheng ◽

Fan Zhang ◽

Tiegang Liu

Keyword(s):

Steady State ◽

Galerkin Method ◽

Least Squares ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Compressible Flows ◽

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A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-015-0022-7 ◽

2015 ◽

Vol 66 (1) ◽

pp. 321-345 ◽

Author(s):

Bo Dong ◽

Chi-Wang Shu ◽

Wei Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

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A modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.06.033 ◽

2019 ◽

Vol 345 ◽

pp. 374-387 ◽

Author(s):

Aimin Chen ◽

Maojun Li

Keyword(s):

Galerkin Method ◽

Shallow Water ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Shallow Water Equations ◽

Positivity Preserving ◽

One Dimensional ◽

Nonlinear Shallow Water Equations ◽

The One ◽

Central Discontinuous Galerkin

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A space discontinuous Galerkin method for the one-dimensional unsteady convection-diffusion equation

Water Resources Management ◽

10.1007/bf00431142 ◽

1990 ◽

Vol 4 (3) ◽

pp. 175-185 ◽

Author(s):

Diamandis N. Karamouzis

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

One Dimensional ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

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Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1105364 ◽

2015 ◽

Vol 94 (2) ◽

pp. 316-344 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Gordon Equation ◽

Local Discontinuous Galerkin Method ◽

Sine Gordon Equation ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Energy Conserving ◽

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Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

Computers & Fluids ◽

10.1016/j.compfluid.2017.06.010 ◽

2017 ◽

Vol 156 ◽

pp. 34-47 ◽

Author(s):

J.S.B. van Zwieten ◽

B. Sanderse ◽

M.H.W. Hendrix ◽

C. Vuik ◽

R.A.W.M. Henkes

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Two Phase Flow ◽

Two Phase ◽

One Dimensional ◽

Efficient Simulation

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A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation

Journal of Computational Physics ◽

10.1016/j.jcp.2018.08.050 ◽

2019 ◽

Vol 376 ◽

pp. 973-991 ◽

Author(s):

Wei Su ◽

Peng Wang ◽

Yonghao Zhang ◽

Lei Wu

Keyword(s):

Steady State ◽

Kinetic Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Hybridizable Discontinuous Galerkin ◽

Convergence To Steady State ◽

Hybridizable Discontinuous Galerkin Method ◽

Steady State Solutions

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Superconvergence of the local discontinuous galerkin method applied to the one-dimensional second-order wave equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21840 ◽

2013 ◽

Vol 30 (3) ◽

pp. 862-901 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation ◽

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High order discontinuous Galerkin method for reduced flow models in fractured porous media

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.07.012 ◽

2021 ◽

Author(s):

Igor Mozolevski ◽

Marcio A. Murad ◽

Luciane A. Schuh

Keyword(s):

Porous Media ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Fractured Porous Media ◽

Flow Models ◽

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