• 论文 • 下一篇
袁光伟
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.
Yuan Guangwei. DIFFUSION SCHEMES SATISFYING EXTREMUM PRINCIPLE ON NONORTHOGONAL MESHES[J]. Mathematica Numerica Sinica, 2021, 43(1): 1-16.
Yuan Guangwei
MR(2010)主题分类:
分享此文:
[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] 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, 2: [3] Nordbotten J M, Aavatsmark I, Eigestad G T. Monotonicity of control volume methods[J]. Numer Math, 2007, 106:255-288. [4] 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. [5] Droniou J. Finite volume schemes for diffusion equations:introduction to and review of modern methods[J]. Math. Mod. Meth. Appl. Sci., 2014, 24:1575-1619. [6] Le Potier C. A nonlinear finite volume scheme satisfying maximum and minimum principles for diffusion operators[J]. Int. J. Finite. Vol Meth, 2009, 6:2. [7] Droniou J, Le Potier C. Construction and convergence study of schemes preserving the elliptic local maximum principle[J]. SIAM J. Numer. Anal., 2011, 49:459-490. [8] Sheng Z, Yuan G. The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes[J]. J. Comput. Phys., 2011, 230:2588-2604. [9] Sheng Z, Yuan G. Construction of nonlinear weighted method for finite volume schemes preserving maximum principle[J]. SIAM J. Sci. Comput., 2018, 40:A607-A628. [10] Yuan G, Yu Y. Existence of solution of a finite volume scheme preserving maximum principle for diffusion equations[J]. Numer. Meth. Part. Diff. Equ., 2018, 34:80-96. [11] Yu Y, Chen X, Yuan G. A Finite Volume Scheme Preserving Maximum Principle for the System of Radiation Diffusion Equations with Three-Temperature[J]. SIAM J. Sci. Comput., 2019, 41:B93-B113. [12] Chang L, Sheng Z, Yuan G. An improvement of the two-point flux approximation scheme on polygonal meshes[J]. J. Comput. Phys., 2019, 392:187-204. [13] Patankar S V. Numerical Heat Transfer and Fluid Flow[M]. McGraw-Hill, New York, 1980. [14] 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. [15] 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]. J. Comput. Phys., 2020, 407:109-143. [16] 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. [17] Le Potier C. A nonlinear correction and maximum principle for diffusion operators discretized using cell-centered finite volume schemes[J]. Comptes Rendus Mathematique, 2010, 348:691-695. [18] Le Potier C, Mahamane A. A nonlinear correction and maximum principle for diffusion operators with hybrid schemes[J]. Comptes Rendus Mathematique, 2012, 350:101-106. [19] Cances C, Cathala M, Le Potier C. Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations[J]. Numer Math, 2013, 125:387-417. [20] Le Potier C. A nonlinear second order in space correction and maximum principle for diffusion operators[J]. Comptes Rendus Mathematique, 2014, 352:947-952. [21] 袁光伟. 扩散方程九点格式中网格节点值的计算与分析[J]. 计算物理实验室年报, 2005, 530-575. [22] Sheng Z, Yuan G. A nine point scheme for the approximation of diffusion operators on distorted quadrilateral meshes. SIAM J. Sci. Comput., 2008, 30:1341-1361. [23] 袁光伟, 岳晶岩, 盛志强, 沈隆钧, 非线性抛物型方程计算方法. 中国科学:数学, 2005, 512-529. [24] Gilbarg D, Trudinger N S. Elliptic Partial Diiferential Equations of Second Order[M]. Springer, 2nd, 2001. [25] Jost J. Partial Diiferential Equations[M]. Springer, 2nd, 2007. [26] Bessemoulin-Chaatard M, Chainais-Hillairet C, Filbet F. On discrete functional inequalities for some finite volume schemes[J]. IMA J Numer Anal, 2014, 1-35. [27] Droniou J, Eymard R, Gallouet T, Herbin R. The Gradient Discretisation Method[M]. Springer, 2018. |
[1] | 邓定文, 赵紫琳. 求解二维Fisher-KPP方程的一类保正保界差分格式及其Richardson外推法[J]. 计算数学, 2022, 44(4): 561-584. |
[2] | 郭洁, 万中. 求解大规模极大极小问题的光滑化三项共轭梯度算法[J]. 计算数学, 2022, 44(3): 324-338. |
[3] | 包学忠, 胡琳, 产蔼宁. 线性随机变时滞微分方程指数Euler方法的收敛性和稳定性[J]. 计算数学, 2022, 44(3): 339-353. |
[4] | 霍振阳, 张静娜, 黄健飞. 多项Caputo分数阶随机微分方程的Euler-Maruyama方法[J]. 计算数学, 2022, 44(3): 354-367. |
[5] | 李步扬. 曲率流的参数化有限元逼近[J]. 计算数学, 2022, 44(2): 145-162. |
[6] | 刘瑶宁. 几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法[J]. 计算数学, 2022, 44(2): 187-205. |
[7] | 杨学敏, 牛晶, 姚春华. 椭圆型界面问题的破裂再生核方法[J]. 计算数学, 2022, 44(2): 217-232. |
[8] | 马玉敏, 蔡邢菊. 求解带线性约束的凸优化的一类自适应不定线性化增广拉格朗日方法[J]. 计算数学, 2022, 44(2): 272-288. |
[9] | 余妍妍, 代新杰, 肖爱国. 非自治刚性随机微分方程正则EM分裂方法的收敛性和稳定性[J]. 计算数学, 2022, 44(1): 19-33. |
[10] | 邵新慧, 亢重博. 基于分数阶扩散方程的离散线性代数方程组迭代方法研究[J]. 计算数学, 2022, 44(1): 107-118. |
[11] | 古振东. 非线性弱奇性Volterra积分方程的谱配置法[J]. 计算数学, 2021, 43(4): 426-443. |
[12] | 包学忠, 胡琳. 随机变延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2021, 43(3): 301-321. |
[13] | 李旭, 李明翔. 连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速[J]. 计算数学, 2021, 43(3): 354-366. |
[14] | 张丽丽, 任志茹. 改进的分块模方法求解对角占优线性互补问题[J]. 计算数学, 2021, 43(3): 401-412. |
[15] | 邱泽山, 曹学年. 带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式[J]. 计算数学, 2021, 43(2): 210-226. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||