Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems
ESAIM: M2AN, 50 4 (2016) 1083-1105
Published online: 2016-07-07
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations
Sigrun OrtlebCommunications on Applied Mathematics and Computation 7 (4) 1195 (2025)
https://doi.org/10.1007/s42967-023-00296-4
The fully-discrete pseudocompressible methods for micropolar Navier–Stokes equations based on local discontinuous Galerkin and Adams–Bashforth–Moulton methods
Demin Liu and Shanshan LiuPhysics of Fluids 37 (4) (2025)
https://doi.org/10.1063/5.0261072
Novel adaptive IMEX two-step Runge-Kutta temporal discretization methods for unsteady flows
Xueyu QIN, Jian YU, Xin ZHANG, Zhenhua JIANG and Chao YANChinese Journal of Aeronautics 103442 (2025)
https://doi.org/10.1016/j.cja.2025.103442
Local discontinuous Galerkin methods with implicit–explicit BDF time marching for Newell–Whitehead–Segel equations
Haijin Wang, Xiaobin Shi, Rumeng Shao, Hongqiang Zhu and Yanping ChenInternational Journal of Computer Mathematics 102 (3) 465 (2025)
https://doi.org/10.1080/00207160.2024.2423658
Higher Order Method Based on the Combination of Local Discontinuous Galerkin and Spectral Deferred Correction Method for the Rotating Navier–Stokes Equations
Xuewei Zhang and Demin LiuInternational Journal for Numerical Methods in Fluids (2025)
https://doi.org/10.1002/fld.5408
Discontinuous Galerkin Method Based on the Reduced Space for the Nonlinear Convection–Diffusion–Reaction Equation
Shijin Hou and Yinhua XiaJournal of Scientific Computing 99 (1) (2024)
https://doi.org/10.1007/s10915-024-02486-5
Boundary Treatment for High-Order IMEX Runge–Kutta Local Discontinuous Galerkin Schemes for Multidimensional Nonlinear Parabolic PDEs
Víctor González-Tabernero, José Germán López-Salas, Manuel Jesús Castro-Díaz and José Antonio García-RodríguezSIAM Journal on Scientific Computing 46 (5) A3282 (2024)
https://doi.org/10.1137/23M1612184
Analysis of Local Discontinuous Galerkin Methods with Implicit-Explicit Time Marching for Linearized KdV Equations
Haijin Wang, Qi Tao, Chi-Wang Shu and Qiang ZhangSIAM Journal on Numerical Analysis 62 (5) 2222 (2024)
https://doi.org/10.1137/24M1635818
Local discontinuous Galerkin method coupled with the implicit‐explicit Runge–Kutta method for the time‐dependent micropolar fluid equations
Mengqi Li and Demin LiuInternational Journal for Numerical Methods in Fluids 96 (7) 1137 (2024)
https://doi.org/10.1002/fld.5282
Ultra-weak discontinuous Galerkin method with IMEX-BDF time marching for two dimensional convection-diffusion problems
Haijin Wang, Lulu Jiang, Qiang Zhang, Yuan Xu and Xiaobin ShiComputers & Mathematics with Applications 176 77 (2024)
https://doi.org/10.1016/j.camwa.2024.09.009
Higher order method based on the coupling of local discontinuous Galerkin method with multistep implicit-explicit time-marching for the micropolar Navier–Stokes equations
Shanshan Liu and Demin LiuPhysics of Fluids 36 (11) (2024)
https://doi.org/10.1063/5.0239069
Local Discontinuous Galerkin Methods with Multistep Implicit–Explicit Time Discretization for Nonlinear Schrödinger Equations
Ying Li, Hui Shi and Xinghui ZhongJournal of Scientific Computing 101 (1) (2024)
https://doi.org/10.1007/s10915-024-02647-6
Error estimates of the local discontinuous Galerkin methods for two-dimensional (μ)-Camassa–Holm equations
Jinyang Lu, Yan Xu and Chao ZhangJournal of Computational and Applied Mathematics 420 114722 (2023)
https://doi.org/10.1016/j.cam.2022.114722
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem
Yao Cheng, Shan Jiang and Martin StynesMathematics of Computation 92 (343) 2065 (2023)
https://doi.org/10.1090/mcom/3844
Optimal pointwise convergence of the LDG method for singularly perturbed convection–diffusion problem
Yao Cheng and Xuesong WangApplied Mathematics Letters 140 108590 (2023)
https://doi.org/10.1016/j.aml.2023.108590
Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit–Explicit Backward Difference Formulas up to Fifth Order for Convection–Diffusion Equation
Haijin Wang, Xiaobin Shi and Qiang ZhangJournal of Scientific Computing 96 (2) (2023)
https://doi.org/10.1007/s10915-023-02264-9
L1/LDG Method for the Generalized Time-Fractional Burgers Equation in Two Spatial Dimensions
Changpin Li, Dongxia Li and Zhen WangCommunications on Applied Mathematics and Computation 5 (4) 1299 (2023)
https://doi.org/10.1007/s42967-022-00199-w
Stability analysis and error estimates of fully-discrete local discontinuous Galerkin methods for simulating wormhole propagation with Darcy–Forchheimer model
Lulu Tian, Hui Guo, Rui Jia and Yang YangJournal of Computational and Applied Mathematics 409 114158 (2022)
https://doi.org/10.1016/j.cam.2022.114158
The Direct Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Marching for Linear Convection-Diffusion Problems
Haijin Wang and Qiang ZhangCommunications on Applied Mathematics and Computation 4 (1) 271 (2022)
https://doi.org/10.1007/s42967-020-00114-1
High-order numerical algorithms for the time-fractional convection–diffusion equation
Zhen WangInternational Journal of Computer Mathematics 99 (11) 2327 (2022)
https://doi.org/10.1080/00207160.2022.2056697
Diffusion study by diffusion quadruple experiment and two-dimensional simulation
Cheng-Hui Xia, Genfeng Shang, Ying Li and Xiao-Gang LuScripta Materialia 216 114760 (2022)
https://doi.org/10.1016/j.scriptamat.2022.114760
Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations
Hui Bi and Yixin ChenJournal of Inequalities and Applications 2022 (1) (2022)
https://doi.org/10.1186/s13660-022-02843-8
A local discontinuous Galerkin method for pattern formation dynamical model in polymerizing action flocks
Lulu Tian, Xiuhui Guo, Hui Guo, et al.Science China Mathematics 65 (4) 849 (2022)
https://doi.org/10.1007/s11425-020-1748-8
Application of digital models for improvement of beef cattle feeding graphs
V. Yu. Sidorova, E. B. Petrov and N. N. NovikovProceedings of the National Academy of Sciences of Belarus. Agrarian Series 60 (4) 380 (2022)
https://doi.org/10.29235/1817-7204-2022-60-4-380-393
The local discontinuous Galerkin finite element method for a multiterm time-fractional initial-boundary value problem
Zhen WangJournal of Applied Mathematics and Computing 68 (6) 4391 (2022)
https://doi.org/10.1007/s12190-021-01608-8
Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations
Xiangyi Meng and Yan XuAdvances in Aerodynamics 4 (1) (2022)
https://doi.org/10.1186/s42774-022-00110-4
Arbitrary Lagrangian–Eulerian Local Discontinuous Galerkin Method for Linear Convection–Diffusion Equations
Lingling Zhou and Yinhua XiaJournal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01697-4
An Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion equations
Joseph Nakao, Jiajie Chen and Jing-Mei QiuJournal of Computational Physics 470 111589 (2022)
https://doi.org/10.1016/j.jcp.2022.111589
Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis
Ruchi Guo and Yulong XingJournal of Scientific Computing 87 (1) (2021)
https://doi.org/10.1007/s10915-021-01418-x
Application of the Discontinuous Galerkin Method to the Study of the Dynamics of Temperature and Pressure Changes in a Formation with an Injection Well and a Hydraulic Fracture
Ruslan V. Zhalnin, Victor F. Masyagin, Elizaveta E. Peskova and Vladimir F. TishkinEngineering Technologies and Systems 31 (1) 161 (2021)
https://doi.org/10.15507/2658-4123.031.202101.161-174
Error estimates of local discontinuous Galerkin method with implicit-explicit Runge Kutta for two-phase miscible flow in porous media
Caixia Nan and Huailing SongApplied Numerical Mathematics 169 334 (2021)
https://doi.org/10.1016/j.apnum.2021.07.009
Time-Accurate and highly-Stable Explicit operators for stiff differential equations
Maxime Bassenne, Lin Fu and Ali ManiJournal of Computational Physics 424 109847 (2021)
https://doi.org/10.1016/j.jcp.2020.109847
A space-time spectral method for the 1-D Maxwell equation
Hui-qing Liao, Ying Fu and He-ping MaAIMS Mathematics 6 (7) 7649 (2021)
https://doi.org/10.3934/math.2021444
Stability and error estimates of local discontinuous Galerkin method with implicit-explicit time marching for simulating wormhole propagation
Hui Guo, Rui Jia, Lulu Tian and Yang YangESAIM: Mathematical Modelling and Numerical Analysis 55 (3) 1103 (2021)
https://doi.org/10.1051/m2an/2021020
A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations
Maojun Li, Yongping Cheng, Jie Shen and Xiangxiong ZhangJournal of Computational Physics 425 109906 (2021)
https://doi.org/10.1016/j.jcp.2020.109906
Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation
Yong Liu, Qi Tao and Chi-Wang ShuESAIM: Mathematical Modelling and Numerical Analysis 54 (6) 1797 (2020)
https://doi.org/10.1051/m2an/2020023
An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives
Qi Tao, Yan Xu and Chi-Wang ShuMathematics of Computation 89 (326) 2753 (2020)
https://doi.org/10.1090/mcom/3562
L2-stability analysis of IMEX-(σ,μ)DG schemes for linear advection-diffusion equations
Sigrun OrtlebApplied Numerical Mathematics 147 43 (2020)
https://doi.org/10.1016/j.apnum.2019.08.016
An $$h-$$Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model
Lulu Tian, Hui Guo, Rui Jia and Yang YangJournal of Scientific Computing 82 (2) (2020)
https://doi.org/10.1007/s10915-020-01135-x
Stability analysis and error estimates of local discontinuous Galerkin methods with semi-implicit spectral deferred correction time-marching for the Allen–Cahn equation
Fengna Yan and Yan XuJournal of Computational and Applied Mathematics 376 112857 (2020)
https://doi.org/10.1016/j.cam.2020.112857
Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems
Haijin Wang, Qiang Zhang and Chi-Wang ShuJournal of Scientific Computing 81 (3) 2080 (2019)
https://doi.org/10.1007/s10915-019-01072-4
Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes
Jie Du, Yang Yang and Eric ChungBIT Numerical Mathematics 59 (4) 853 (2019)
https://doi.org/10.1007/s10543-019-00757-4
High-order local discontinuous Galerkin method for simulating wormhole propagation
Hui Guo, Lulu Tian, Ziyao Xu, Yang Yang and Ning QiJournal of Computational and Applied Mathematics 350 247 (2019)
https://doi.org/10.1016/j.cam.2018.10.021
Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation
Hui Shi and Ying LiJournal of Computational Physics 394 719 (2019)
https://doi.org/10.1016/j.jcp.2019.05.040
Fourier Analysis of Local Discontinuous Galerkin Methods for Linear Parabolic Equations on Overlapping Meshes
Nattaporn Chuenjarern and Yang YangJournal of Scientific Computing 81 (2) 671 (2019)
https://doi.org/10.1007/s10915-019-01030-0
Local Discontinuous Galerkin Method with Implicit–Explicit Time Marching for Incompressible Miscible Displacement Problem in Porous Media
Haijin Wang, Jingjing Zheng, Fan Yu, Hui Guo and Qiang ZhangJournal of Scientific Computing 78 (1) 1 (2019)
https://doi.org/10.1007/s10915-018-0752-4
Stability Analysis and Error Estimates of Semi-implicit Spectral Deferred Correction Coupled with Local Discontinuous Galerkin Method for Linear Convection–Diffusion Equations
Lingling Zhou and Yan XuJournal of Scientific Computing 77 (2) 1001 (2018)
https://doi.org/10.1007/s10915-018-0735-5
Third order implicit–explicit Runge–Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection–diffusion problems with Dirichlet boundary conditions
Haijin Wang, Qiang Zhang and Chi-Wang ShuJournal of Computational and Applied Mathematics 342 164 (2018)
https://doi.org/10.1016/j.cam.2018.04.004
Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media
Hui Guo, Fan Yu and Yang YangJournal of Scientific Computing 71 (2) 615 (2017)
https://doi.org/10.1007/s10915-016-0313-7
Local Discontinuous Galerkin Method for the Keller-Segel Chemotaxis Model
Xingjie Helen Li, Chi-Wang Shu and Yang YangJournal of Scientific Computing 73 (2-3) 943 (2017)
https://doi.org/10.1007/s10915-016-0354-y
Unconditional Energy Stability Analysis of a Second Order Implicit–Explicit Local Discontinuous Galerkin Method for the Cahn–Hilliard Equation
Huailing Song and Chi-Wang ShuJournal of Scientific Computing 73 (2-3) 1178 (2017)
https://doi.org/10.1007/s10915-017-0497-5
1863 020006 (2017)
https://doi.org/10.1063/1.4992152
Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs
Haijin Wang, Qiang Zhang and Chi-Wang ShuESAIM: Mathematical Modelling and Numerical Analysis 51 (5) 1931 (2017)
https://doi.org/10.1051/m2an/2017017
Conservative Local Discontinuous Galerkin Method for Compressible Miscible Displacements in Porous Media
Fan Yu, Hui Guo, Nattaporn Chuenjarern and Yang YangJournal of Scientific Computing 73 (2-3) 1249 (2017)
https://doi.org/10.1007/s10915-017-0571-z