细菌模型的非协调混合有限元分析
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摘要
文章对细菌模型构造了一个新的三维非协调混合元逼近格式,首先证明了逼近解的存在唯一性。其次,借助于该单元的一些特性,利用对时间t导数转移的技巧以及插值后处理技术,在半离散格式下分别导出了原始变量u,v的H1模和中间变量p,q的L2模下O(h2)阶超逼近性质和整体超收敛。此外,通过构造适当的全离散格式,对边界项的估计利用分裂技巧,得到了精度为O(h2+Δt)误差估计结果。
A new three-dimensional nonconforming mixed finite element method is constructed for Bacterial Model.First,the existence and uniqueness of approximation solution are proved.Secondly,by utilizing the properties of interpolation on the element,derivative delivery techniques with respect to time t and interpolated postprocessing approach,the superclose properties and the global superconvergence with order O(h2)for the primitive solution u,vin broken H1 norm and the intermediate variable p,qin L2 norm are obtained respectively for semi-discrete scheme.Moreover,by utilizing splitting techniques,the error estimates results with order O(h2+Δt)are obtained through constructing a new full-discrete scheme.
A new three-dimensional nonconforming mixed finite element method is constructed for Bacterial Model.First,the existence and uniqueness of approximation solution are proved.Secondly,by utilizing the properties of interpolation on the element,derivative delivery techniques with respect to time t and interpolated postprocessing approach,the superclose properties and the global superconvergence with order O(h2)for the primitive solution u,vin broken H1 norm and the intermediate variable p,qin L2 norm are obtained respectively for semi-discrete scheme.Moreover,by utilizing splitting techniques,the error estimates results with order O(h2+Δt)are obtained through constructing a new full-discrete scheme.
引文
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[6]张争茹.带有迁移的疟疾病和疟蚊数学模型的交替方向有限元方法及数值分析[J].生物数学学报,2003,18(1):429-433.
[7]曲凤龙,王玉泉.一类带有趋化性扩散的细菌模型一致有界解的整体存在性[J].数学物理学报,2014,34A(2):409-418.
[8]许超群,李宏恩,原三领.一类噬菌体死亡率受到噪声干扰的随机噬菌体-细菌模型研究[J].高校应用数学学报,2015,30(3):253-261.DIO:10.13299/j.cnki.amjcu.001883.
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[10]陈绍春,陈红如.二阶椭圆问题新的混合元格式[J].计算数学,2010,32(2):213-218.
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[13]张厚超,石东洋.非线性四阶双曲方程低阶混合元方法的超收敛分析[J].数学物理学报,2016,36A(4):656-671.
[14]张厚超,毛凤梅,白秀琴.广义神经传播方程新的非协调混合元方法的超逼近分析[J].四川师范大学学报(自然科学版),2017,40(4):464-472.
[15]张厚超,石东洋.EFK方程一个新的低阶非协调混合有限元方法的高精度分析[J].高校应用数学学报,2017,32(4):437-454.DOI:10.13299/j.cnki.amicu.001997.
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[17] Lin Q,Lin J F.Finie Element Methods:Accuracy and Improvement[M].Beijing:Science Press,China,2006.
[18] Shi D Y,Mao S P,Chen S C.Anisotropic Nonconforming Finite Element with Some Superconvergence Results[J].J Comput Math,2005,3(3):261-274.DOI:http:∥www.jstor.org/stable/43693234.
[19] Hale J K.Ordinary Differential Equations[M].New York:Wiley-Inter Science,1969.
[2]陈仲慈.推广的细菌模型的周期边界问题[J].高校应用数学学报A辑,1987,2(4):559-566.DOI:10.13299/j.cnki.amjcu.000142.
[3] Liu B P,Pao C V.Almost Periodic Plane Wave Solutions for Reaction Diffusion Equations[J].J Math Anal Appl,1985,105(1):231-249.DOI:https:∥doi.org/10.1016/0022-247X(85)90109-X.
[4]吕淑娟,李路,张仲.一类广义细菌模型的定解问题[J].生物数学学报,1997,12(5):429-433.
[5]吕淑娟,张仲.二维广义细菌模型的周期初值问题[J].数理医药杂志,1997,10(3):198-200.
[6]张争茹.带有迁移的疟疾病和疟蚊数学模型的交替方向有限元方法及数值分析[J].生物数学学报,2003,18(1):429-433.
[7]曲凤龙,王玉泉.一类带有趋化性扩散的细菌模型一致有界解的整体存在性[J].数学物理学报,2014,34A(2):409-418.
[8]许超群,李宏恩,原三领.一类噬菌体死亡率受到噪声干扰的随机噬菌体-细菌模型研究[J].高校应用数学学报,2015,30(3):253-261.DIO:10.13299/j.cnki.amjcu.001883.
[9]石东洋,裴丽芳.细菌模型的非协调有限元分析[J].应用数学学报,2011,34(3):428-439.
[10]陈绍春,陈红如.二阶椭圆问题新的混合元格式[J].计算数学,2010,32(2):213-218.
[11]史峰,于佳平,李开泰.椭圆方程的一种新型混合元格式[J].工程数学学报,2011,82(2):231-237.
[12]石东洋,李明浩.阶椭圆问题一种新格式的高精度分析[J].应用数学学报,2014,37(1):45-58.
[13]张厚超,石东洋.非线性四阶双曲方程低阶混合元方法的超收敛分析[J].数学物理学报,2016,36A(4):656-671.
[14]张厚超,毛凤梅,白秀琴.广义神经传播方程新的非协调混合元方法的超逼近分析[J].四川师范大学学报(自然科学版),2017,40(4):464-472.
[15]张厚超,石东洋.EFK方程一个新的低阶非协调混合有限元方法的高精度分析[J].高校应用数学学报,2017,32(4):437-454.DOI:10.13299/j.cnki.amicu.001997.
[16] Shi D Y,Zhang Y D.High Accuracy Analysis of a New Nonconforming Mix Finite Element Scheme for Sobolev Equations[J].Appl Math Comput,2011,218(7):3176-3186.DOI:https:∥doi.org/10.1016/j.amc.2011.08.054.
[17] Lin Q,Lin J F.Finie Element Methods:Accuracy and Improvement[M].Beijing:Science Press,China,2006.
[18] Shi D Y,Mao S P,Chen S C.Anisotropic Nonconforming Finite Element with Some Superconvergence Results[J].J Comput Math,2005,3(3):261-274.DOI:http:∥www.jstor.org/stable/43693234.
[19] Hale J K.Ordinary Differential Equations[M].New York:Wiley-Inter Science,1969.