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• Derivation of Asymptotic Limiting Equations for Multigroup Anisotropic-Scattering Transport Processes in Optically Thick Regimes

  Weiming Li, Chang Liu, Peng Song

  2026-01-03

  1670 60 Pages:919-940

• Reconstructed Discontinuous Galerkin Methods for Hyperbolic Diffusion Equations on Unstructured Grids

  Jialin Lou, Xiaodong Liu, Hong Luo & Hiroaki Nishikawa

  2019-01-10

  50928 4058 Pages:1302-1327

• A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations

  K. B. Nakshatrala, H. Nagarajan & M. Shabouei

  2018-04-03

  40388 4661 Pages:53-93

• The Finite Point Method for Solving the 2-D 3-T Diffusion Equations

  Guixia Lv & Longjun Shen

  2019-04-04

  45129 3344 Pages:413-433

• New Splitting Methods for Convection-Dominated Diffusion Problems and Navier-Stokes Equations

  Feng Shi, Guoping Liang, Yubo Zhao & Jun Zou

  2014-11-08

  41223 3898 Pages:1239-1262

• Do We Need Decay-Preserving Error Estimate for Solving Parabolic Equations with Initial Singularity?

  Jiwei Zhang, Zhimin Zhang, Chengchao Zhao

  2026-01-18

  250 70 Pages:1027-1058

• Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients

  Kejia Pan, Xiaoxin Wu, Yunlong Yu, Zhiqiang Sheng, Guangwei Yuan

  2022-05-06

  44481 3152 Pages:1561-1584

• A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations

  Fei Zhao, Xiang Lai, Guangwei Yuan, Zhiqiang Sheng

  2020-02-23

  47487 3228 Pages:1201-1233

• A Symmetric Direct Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations

  Huiqiang Yue, Jian Cheng & Tiegang Liu

  2018-04-09

  42581 3248 Pages:375-392

• A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media

  Ji Lin, Sergiy Reutskiy, C. S. Chen & Jun Lu

  2019-02-25

  47337 5497 Pages:233-264

• Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection

  S. G. Ayodele, D. Raabe & F. Varnik

  2020-07-31

  41232 4453 Pages:741-756

• Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations

  Xiao-Qing Jin, Fu-Rong Lin & Zhi Zhao

  2018-04-03

  38686 3133 Pages:469-488

• The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle

  Ang Li, Hongtao Yang, Yonghai Li, Guangwei Yuan

  2023-01-24

  37785 3048 Pages:1437-1473

• Upwind Biased Local RBF Scheme with PDE Centres for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions

  K. Monysekar, Y. V. S. S. Sanyasiraju

  2019-12-07

  45099 3142 Pages:460-479

• A Conservative and Positivity-Preserving Method for Solving Anisotropic Diffusion Equations with Deep Learning

  Hui Xie, Li Liu, Chuanlei Zhai, Xuejun Xu, Heng Yong

  2024-03-13

  26287 2282 Pages:467-497

• Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

  S. Karimi & K. B. Nakshatrala

  2018-04-04

  39688 3199 Pages:374-404

• A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

  Jehanzeb Hameed Chaudhry, Jeffrey Comer, Aleksei Aksimentiev & Luke N. Olson

  2014-01-05

  40610 4210 Pages:93-125

• A $H^T_N$-Based UGKS Scheme for the Three-Temperature Radiative Transfer Equations

  Qi Li, Song Jiang, Wenjun Sun

  2025-08-08

  4583 457 Pages:317-347

• A Sylvester-Based IMEX Method via Differentiation Matrices for Solving Nonlinear Parabolic Equations

  Francisco de la Hoz & Fernando Vadillo

  2013-10-05

  38513 3840 Pages:1001-1026

• Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

  Bofeng Liu, Lixing Zhu, Zixuan Yang, Guowei He

  2023-03-13

  41178 3454 Pages:425-451

• A Physics-Wise Splitting Preconditioner with Selective Relaxation for the Multi-Group Radiation Diffusion Equations in Three Dimensions

  Xiaoqiang Yue, Junbai Hou, Long Yuan, Xiaowen Xu, Shi Shu

  2025-08-08

  4540 430 Pages:467-490

• Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

  Xiaoqiang Yue, Jianmeng He, Xiaowen Xu, Shi Shu, Libo Wang

  2022-09-29

  41701 3304 Pages:829-849

• An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes

  Shuai Su, Huazhong Tang, Jiming Wu

  2021-05-25

  48749 3133 Pages:448-485

• Algebraic Multigrid Block Preconditioning for Multi-Group Radiation Diffusion Equations

  Xiaoqiang Yue, Shulei Zhang, Xiaowen Xu, Shi Shu, Weidong Shi

  2021-01-13

  45898 3243 Pages:831-852

• A Decoupled and Positivity-Preserving DDFVS Scheme for Diffusion Problems on Polyhedral Meshes

  Qiannan Dong, Shuai Su, Jiming Wu

  2020-05-06

  50181 3663 Pages:1378-1412

• A Posteriori Error Estimates of Discontinuous Streamline Diffusion Methods for Transport Equations

  Juan Sun, Zhaojie Zhou & Huipo Liu

  2018-09-17

  44601 3599 Pages:1355-1374

• Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations

  Xiaoqiang Yue, Shi Shu, Junxian Wang & Zhiyang Zhou

  2018-08-21

  46726 3289 Pages:540-560