袁光伟
袁光伟. 扩散方程九点格式的保正性与极值性[J]. 数值计算与计算机应用, 2021, 42(2): 134-145.
Yuan Guangwei. POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 134-145.
Yuan Guangwei
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[1] 李德元, 水鸿寿, 汤敏君, 关于非矩形网格上的二维抛物型方程的差分格式[J]. 数值计算与计算机应用, 1980, 1: 217–224 [2] Kershaw D S, Differencing of the diffusion equation in Lagrangian hydrodynamic codes[J]. J Comput Phys, 1981, 39: 375–395 [3] Aavatsmark I, Comparison of Monotonicity for some Multipoint Flux Approximation Methods[J]. R. Eymard, J.-M. Hérard (Editors), Finite Volumes for Complex Applications, Wiley-ISTE, 2008, 5: 19–34 [4] Lipnikov K, Manzini G, Svyatskiy D, Monotonicity Conditions in the Mimetic Finite Difference Method. Springer Proceedings in Mathematics “Finite Volumes for Complex Applications VI Problems & Perspectives”, Volume 1, J. Fort, J. Furst, J. Halama, R. Herbin, F. Hubert (Editors), Springer, pp. 653–662 [5] Nordbotten J M, Aavatsmark I, Eigestad G T. Monotonicity of control volume methods[J]. Numer Math, 2007, 106: 255–288. [6] Sharma P, Hammett G W. Preserving monotonicity in anisotropic diffusion[J]. J Comput Phys, 2007, 227: 123–142. [7] Kuzmin D, Shashkov M J, Svyatskiy D. A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems[J]. J Comput Phys, 2009, 228: 3448–3463. [8] 袁光伟. 扩散方程九点格式中网格节点值的计算与分析. 计算物理实验室年报, 2005, 512–529. [9] 常利娜, 袁光伟, 曾清红. 非匹配网格上求解扩散方程的高精度结点值重构算法[J]. 数值计算与计算机应用, 2016, 37: 57–66. [10] 符尚武, 付汉清, 沈隆钧, 黄书科, 陈光南. 二维三温能量方程的九点差分格式及其迭代解法[J]. 计算物理, 1998, 15(4): 489–497. [11] Blanc X, Despres B. Numerical methods for inertial confinement fusion. Lecture Notes of CEMRACS-10 Summer School: smai.emath.fr/cemracs/cemracs10/fr courses.html, 2010. [12] 王竹溪. 热力学[M]. 第二版, 北京大学出版社, 2005. %吴大猷, 热力学、气体运动论及统计学. 科学出版社, 2005. [13] Gilbarg D, Trudinger N S. Elliptic Partial Diiferential Equations of Second Order. Springer, 2nd, 2001. [14] Jost J. Partial Diiferential Equations. Springer, 2nd, 2007. [15] Patankar S V. Numerical Heat Transfer and Fluid Flow[M]. McGraw-Hill, New York, 1980. [16] Burchard H, Deleersnijder E, Meister A. A high-order conservative Patankar-type discretisation for stiff systems of production-destruction equations[J]. Appl Numer Math, 2003, 47: 1–30. [17] Gao Y, Yuan G, Wang S, Hang X. A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes[J]. Journal of Computational Physics, 2020, 407: 109–143. [18] 袁光伟, 岳晶岩, 盛志强, 沈隆钧. 非线性抛物型方程计算方法[J]. 中国科学: 数学, 2013, 43: 235–248. [19] Yao Y, Yuan G. Enforcing positivity with conservation for nine-point scheme of nonlinear diffusion equations[J]. Comput Methods Appl Mech Engrg, 2012, 223-224: 161–172. [20] Sheng Z, Yuan G[J]. The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes[J]. J. Comput. Phys., 2011, 230: 2588–2604. [21] Wang S, Hang X, Yuan G. A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes[J]. J. Comput. Phys., 2017, 350: 590–606. [22] 袁光伟. 扭曲网格上扩散方程九点格式的构造与分析. 计算物理实验室年报, 2005, 530–575. [23] Sheng Z, Yuan G. A nine point scheme for the approximation of diffusion operators on distorted quadrilateral meshes[J]. SIAM J. Sci. Comput., 2008, 30: 1341–1361. [24] Droniou J. Finite volume schemes for diffusion equations: introduction to and review of modern methods[J]. Math Models Methods Appl Sci (M3AS), 2014, 24: 1575–1619. [25] Bertolazzi E, Manzini G. A second-order maximum principle preserving volume method for steady convection-diffusion problems[J]. SIAM J. Numer. Anal., 2005, 43: 2172–2199. [26] Droniou J, Potier C Le. Construction and convergence study of schemes preserving the elliptic local maximum principle[J]. SIAM J. Numer. Anal., 2011, 49: 459–490. [27] Blanc X, Labourasse E. A positive scheme for diffusion problems on deformed meshes[J]. ZAMM. Z. Angew. Math. Mech., 2016, 96: 660–680. [28] Agélas L, Enchéry G, Flemisch B, Schneider M. Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes[J]. J. Comp. Phys., 2017351: 80–107. [29] 袁光伟. 非正交网格上满足极值原理的扩散格式[J]. 计算数学, 2021, 43(1): 1–16. |
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