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两点混合边值问题的紧有限体积格式 被引量：6

Compact Finite Volume Scheme for Two Point Problem with Mixed Boundary Conditions
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摘要 本文针对常系数和变系数两点混合边值问题提出一种紧有限体积格式,该格式形成的线性代数方程组具有三对角性质,可以使用追赶法求解.证明格式按照H1半范数具有四阶收敛精度.利用节点计算值,给出单元中点值和一阶导数值的高精度后处理计算公式,这两个公式同样具有四阶精度.数值算例验证了理论分析的正确性,并说明了格式的有效性. In this paper,a compact finite volume scheme is proposed for mixed two point boundary value problems with both constant coefficient and variable coefficient.The linear algebraic system derived by this scheme has tridiagonal property and can be solved by Thomas method.It is proved that the given scheme is convergent with fourth-order accuracy according to H1 discrete seminorm.Furthermore,the post-processing formulas for the numerical value and derivative at midpoint of every element are obtained,which both have fourth order accuracy.Numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme.
作者 崔吉田 王同科
机构地区 天津师范大学数学科学学院
出处 《应用数学》 CSCD 北大核心 2012年第1期96-104,共9页 Mathematica Applicata
基金 国家自然科学基金资助项目(11071123)
关键词 两点混合边值问题 紧有限体积格式 误差估计 高精度后处理公式 Two point problem with mixed boundary conditions Compact finite volume scheme Error estimate Hight accuracy post-processing formula
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献14

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二级参考文献26

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共引文献25

同被引文献46

  • 1秦经刚,王同科,王彩华.常系数对流扩散方程的高精度差分格式[J].天津师范大学学报（自然科学版）,2006,26(4):48-50. 被引量：2
  • 2陈传淼.Galerkin解的外推法.湘潭大学学报,1981,2(4):1-6.
  • 3王军平 林群.有限元方法的渐近展开及其外推.系统科学与数学,5(2):114-120.
  • 4朱起定,林群.有限元超收敛理论[M].长沙:湖南科学技术出版社,1989.
  • 5Sun Zhizhong. An unconditionally stable and O(-2 + ha) order Lo convergent difference scheme for linear parabolic equations with variable coefficients[J]. Numerical Methods for Partial Differ- ential Equations, 2001, 17(6): 619-631.
  • 6Qin Jinggang, Wang Tongke. A compact locally one-dimensional finite difference method for nonhomogeneous parabolic differential equations[J]. International Journal for Numerical Methods in Biomedical Engineering, 2011, 27: 128-142.
  • 7Li J, Chen Y, Liu G. High-order compact ADI methods for parabolic equations[J]. Computers and Mathematics with Applications, 2006, 52: 1343-1356.
  • 8Zhao Jennifer, Dai Weizhong, Niu Tianchan. Fourth-order compact schemes of a heat conduc- tion problem with Neumann boundary condition[J]. Numerical Methods for Partial Differential Equations, 2007, 23: 949-959.
  • 9Sun Zhizhong. Compact difference schemes for heat equation with Neumann boundary condi- tions[J]. Numerical Methods for Partial Differential Equations, 2009, 25: 1320-1341.
  • 10Liao W Y, Zhu J P, and Khaliq A Q M. A fourth-order compact algorithm for nonlinear reac- tion diffusion equations with Neumann boundary conditions[J]. Numerical Methods for Partial Differential Equations, 2006, 22: 600-616.

引证文献6

二级引证文献10

应用数学
2012年 第1期

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