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A uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface
1. | Department of Mathematics, University of Wisconsin, Madison, WI 53706 |
2. | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China, China |
[1] |
Giada Basile, Tomasz Komorowski, Stefano Olla. Diffusion limit for a kinetic equation with a thermostatted interface. Kinetic and Related Models, 2019, 12 (5) : 1185-1196. doi: 10.3934/krm.2019045 |
[2] |
Liu Liu. Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scaling. Kinetic and Related Models, 2018, 11 (5) : 1139-1156. doi: 10.3934/krm.2018044 |
[3] |
Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a two-scale linear transport equation. Networks and Heterogeneous Media, 2006, 1 (1) : 143-166. doi: 10.3934/nhm.2006.1.143 |
[4] |
Markus Gahn. Singular limit for reactive transport through a thin heterogeneous layer including a nonlinear diffusion coefficient. Communications on Pure and Applied Analysis, 2022, 21 (1) : 61-82. doi: 10.3934/cpaa.2021167 |
[5] |
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4907-4926. doi: 10.3934/dcdsb.2020319 |
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Stefan Possanner, Claudia Negulescu. Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport. Kinetic and Related Models, 2011, 4 (4) : 1159-1191. doi: 10.3934/krm.2011.4.1159 |
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Shi Jin, Xu Yang, Guangwei Yuan. A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface. Kinetic and Related Models, 2008, 1 (1) : 65-84. doi: 10.3934/krm.2008.1.65 |
[8] |
Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure and Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001 |
[9] |
Jisheng Kou, Huangxin Chen, Xiuhua Wang, Shuyu Sun. A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2021094 |
[10] |
Alina Chertock, Changhui Tan, Bokai Yan. An asymptotic preserving scheme for kinetic models with singular limit. Kinetic and Related Models, 2018, 11 (4) : 735-756. doi: 10.3934/krm.2018030 |
[11] |
Hélène Hivert. Numerical schemes for kinetic equation with diffusion limit and anomalous time scale. Kinetic and Related Models, 2018, 11 (2) : 409-439. doi: 10.3934/krm.2018019 |
[12] |
Matthieu Alfaro, Arnaud Ducrot. Sharp interface limit of the Fisher-KPP equation. Communications on Pure and Applied Analysis, 2012, 11 (1) : 1-18. doi: 10.3934/cpaa.2012.11.1 |
[13] |
Pedro Aceves-Sánchez, Christian Schmeiser. Fractional diffusion limit of a linear kinetic equation in a bounded domain. Kinetic and Related Models, 2017, 10 (3) : 541-551. doi: 10.3934/krm.2017021 |
[14] |
Qiang Du, Manlin Li. On the stochastic immersed boundary method with an implicit interface formulation. Discrete and Continuous Dynamical Systems - B, 2011, 15 (2) : 373-389. doi: 10.3934/dcdsb.2011.15.373 |
[15] |
Karl Kunisch, Markus Müller. Uniform convergence of the POD method and applications to optimal control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4477-4501. doi: 10.3934/dcds.2015.35.4477 |
[16] |
Jean-François Coulombel, Frédéric Lagoutière. The Neumann numerical boundary condition for transport equations. Kinetic and Related Models, 2020, 13 (1) : 1-32. doi: 10.3934/krm.2020001 |
[17] |
Lizhi Ruan, Changjiang Zhu. Boundary layer for nonlinear evolution equations with damping and diffusion. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 331-352. doi: 10.3934/dcds.2012.32.331 |
[18] |
Champike Attanayake, So-Hsiang Chou. An immersed interface method for Pennes bioheat transfer equation. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 323-337. doi: 10.3934/dcdsb.2015.20.323 |
[19] |
Bhargav Kumar Kakumani, Suman Kumar Tumuluri. Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 407-419. doi: 10.3934/dcdsb.2017019 |
[20] |
Shu Wang, Chundi Liu. Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2177-2199. doi: 10.3934/cpaa.2017108 |
2020 Impact Factor: 1.213
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