删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

非正交网格上满足极值原理的扩散格式

本站小编 Free考研考试/2021-12-27

袁光伟
北京应用物理与计算数学研究所, 北京8009信箱, 北京 100094
收稿日期:2020-03-10出版日期:2021-02-15发布日期:2021-02-04


基金资助:国家自然科学基金(批准号:11971069)和科学挑战专题(TZ2016002)资助.

DIFFUSION SCHEMES SATISFYING EXTREMUM PRINCIPLE ON NONORTHOGONAL MESHES

Yuan Guangwei
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China
Received:2020-03-10Online:2021-02-15Published:2021-02-04







摘要



编辑推荐
-->


构造了非正交网格上扩散方程新的非线性单元中心型有限体积格式, 证明了该格式满足离散极值原理, 且在适当条件下具有强制性、以及在离散H1范数下解的有界性和一阶收敛性.
MR(2010)主题分类:
65M06
65M12
65N08
65N12
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]朱梦姣, 王文强. 非线性随机分数阶微分方程Euler方法的弱收敛性[J]. 计算数学, 2021, 43(1): 87-109.
[2]李天怡, 陈芳. 求解一类分块二阶线性方程组的QHSS迭代方法[J]. 计算数学, 2021, 43(1): 110-117.
[3]古振东, 孙丽英. 非线性第二类Volterra积分方程的Chebyshev谱配置法[J]. 计算数学, 2020, 42(4): 445-456.
[4]尹江华, 简金宝, 江羡珍. 凸约束非光滑方程组一个新的谱梯度投影算法[J]. 计算数学, 2020, 42(4): 457-471.
[5]唐斯琴, 李宏, 董自明, 赵智慧. 对流反应扩散方程的稳定化时间间断时空有限元解的误差估计[J]. 计算数学, 2020, 42(4): 472-486.
[6]张纯, 贾泽慧, 蔡邢菊. 广义鞍点问题的改进的类SOR算法[J]. 计算数学, 2020, 42(1): 39-50.
[7]李枝枝, 柯艺芬, 储日升, 张怀. 二阶锥线性互补问题的广义模系矩阵分裂迭代算法[J]. 计算数学, 2019, 41(4): 395-405.
[8]张燕美, 兰斌, 盛志强, 袁光伟. 非定常对流扩散方程保正格式解的存在性[J]. 计算数学, 2019, 41(4): 381-394.
[9]贾东旭, 盛志强, 袁光伟. 扩散方程一种无条件稳定的保正并行有限差分方法[J]. 计算数学, 2019, 41(3): 242-258.
[10]胡冬冬, 曹学年, 蒋慧灵. 带非线性源项的双侧空间分数阶扩散方程的隐式中点方法[J]. 计算数学, 2019, 41(3): 295-307.
[11]盛秀兰, 赵润苗, 吴宏伟. 二维线性双曲型方程Neumann边值问题的紧交替方向隐格式[J]. 计算数学, 2019, 41(3): 266-294.
[12]岳超. 高阶分裂步(θ1,θ2,θ3)方法的强收敛性[J]. 计算数学, 2019, 41(2): 126-155.
[13]杨晋平, 李志强, 闫玉斌. 求解Riesz空间分数阶扩散方程的一种新的数值方法[J]. 计算数学, 2019, 41(2): 170-190.
[14]张维, 王文强. 随机微分方程改进的分裂步单支θ方法的强收敛性[J]. 计算数学, 2019, 41(1): 12-36.
[15]王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=5083
相关话题/计算 数学 分数 北京 空间