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一类二维粘性波动方程的交替方向有限体积元方法 被引量：5

AN ALTERNATING DIRECTION FINITE VOLUME ELEMENT METHOD FOR A CLASS OF TWO-DIMENSIONAL VISCOUS WAVE EQUATIONS
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摘要 针对二维粘性波动方程模型问题,提出了一类基于双线性插值的交替方向有限体积元方法,并给出了两种具体计算格式,一是基于有限差分方法中Douglas思想的格式,二是一类推广型的局部一维格式.分析证明了该方法按照L^2范数在时间和空间方向均有二阶收敛精度.最后,数值算例验证了算法的有效性和精确性. An alternating direction finite volume element method based on bilinear interpolation is presented for a class of two-dimensional viscous wave equations and two concrete computational schemes are given, one is similar to Douglas scheme in finite difference and the other is an extended locally one-dimensional scheme. It is proved that the method has second order accuracy both in temporal and spatial directions with respect to L^2 norm. Finally, a numerical example is provided to demonstrate the efficiency and accuracy of the method.
作者 王同科
机构地区 天津师范大学数学科学学院
出处 《数值计算与计算机应用》 CSCD 北大核心 2010年第1期64-75,共12页 Journal on Numerical Methods and Computer Applications
关键词 二维粘性波动方程 交替方向方法 有限体积元方法 收敛性 误差估计 two-dimensional viscous wave equation alternating direction method finite volume element method convergence error estimate
分类号 O241.82 [理学—计算数学]
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参考文献18

  • 1Jim Douglas, Jr, Seongjai Kim and Hyeona Lim. An improved alternating-direction method for a viscous wave equation[C]. Z. Chen, R. Glowinski and Kaitai Li. Current Trends in Scientific Computing, Contemporary Mathematics, 2003, 329: 99-104.
  • 2Weizhong Dai, Raja Nassar. A compact finite-difference scheme for solving a one-dimensional heat transport equation at the microscale[J]. Journal of Computational and Applied Mathematics, 2001, 132: 431-441.
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  • 4Jun Zhang, Jennifer J Zhao. Unconditionally stable finite difference scheme and iterative solution of 2D microscale heat transport equation[J]. Journal of Computational Physics, 2001, 170: 261- 275.
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  • 6Zhiqiang Cai, Steve McCormick. On the accuracy of the finite volume element method for diffusion equations on composite grid[J]. SIAM J. Numer. Anal., 1990, 27(3): 636-655.
  • 7王同科.一维二阶椭圆和抛物型微分方程的高精度有限体积元方法[J].数值计算与计算机应用,2002,23(4):264-274. 被引量：11
  • 8Jones W P, Menziest K R. Analysis of the cell-centred finite volume method for the diffusion equation[J]. Journal of Computational Physics, 2000, 165: 45-68.
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  • 10Tongke Wang. A mixed finite volume element method based on rectangular mesh for biharmonic equations[J]. Journal of Computational and Applied Mathematics, 2004, 172: 117-130.

二级参考文献14

  • 1祝丕琦 李荣华.二阶椭圆偏微分方程的广义差分析（II）--四边形网情形[J].高校计算数学学报,1982,4:360-375.
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  • 5Jim Douglas Jr, Gunn J E. A general formulation of alternating direction methods: Part Ⅰ,Parabolic and hyperbolic problems. Numer. Math.,1964, 6:428-453
  • 6Jim Douglas Jr, Seongjal Kim. Improved accuracy for locally one-dimensional methods for parabolic equations. Math. Models Methods Appl. Sci., 2001,11(9): 1563-1579
  • 7Yanenko N N. The method of fractional steps. Springer-Verlag, New York, 1970
  • 8Morris J Lh, Gourlay A R. Modified locally one-dimensional methods for parabolic partial differential equations in two space variables. J. Inst. Math. Appl., 1973, 12:349
  • 9Thomas J W. Numerical partial differential equations(finite difference methods). Springer-Verlag. Reprinted in China by Beijing World Publishing Corporation, 1997
  • 10Jim Douglas Jr, Dupont T. Alternating-direction Galerkin methods on rectangles. Proceedings Symposium on Numerical Solution of Partial Differential Equations, Ⅱ, B.Hubbard ed.,Academic Press, New York, 1971, 133-214

共引文献38

同被引文献32

引证文献5

二级引证文献11

数值计算与计算机应用
2010年 第1期

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