On the stability of some flux splitting schemes

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• 作者：K. V. Voronin ; Yu. M. Laevsky
• 关键词：heat transfer ; mixed formulation ; finite element method ; splitting scheme
• 刊名：Numerical Analysis and Applications
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：8
• 期：2
• 页码：113-121
• 全文大小：528 KB
• 参考文献：1.Voronin, K.V. and Laevsky, Yu.M., An Approach to the Construction of Flow Splitting Schemes in the Mixed Finite Element Method, Mat. Mod., 2014, Vol. 26, No. 12, pp. 33-7.
  2.Gulin, A.V., Stability of Nonlocal Difference Schemes in a Subspace, Diff. Eq., 2012, Vol. 48, No. 7, pp. 956-65.MathSciNet
  3.Arbogast, T., Huang, C.-S., and Yang, S.-M., Improved Accuracy for Alternating-Direction Methods for Parabolic Equations Based on Regular andMixed Finite Elements, Math. Models Methods Appl. Sci., 2007, vol. 17, iss. 8, pp. 1279-305.MATH MathSciNet View Article
  4.Vabishchevich, P.N., Flux-Splitting Schemes for Parabolic Problems, Comp. Math. Math. Phys., 2012, Vol. 52, No. 8, pp. 1415-425.MATH MathSciNet View Article
  5.Voronin, K.V. and Laevsky, Yu.M., Splitting Schemes in Mixed Finite Element Method for a Solution to Heat Transfer Problem, Mat. Mod., 2012, Vol. 24, No. 8, pp. 109-20.MATH
  6.Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods, New York: Springer-Verlag, 1991.MATH View Article
  7.Samarskii, A.A., Vvedenie v teoriyu raznostnykh skhem (Introduction to the Theory of Difference Schemes), Moscow: Nauka, 1971.
  8.Douglas, J. and Gunn, J.E., A General Formulation of Alternating Direction Methods, Num. Math., 1964, Vol. 6, pp. 428-53.MATH MathSciNet View Article
  
• 作者单位：K. V. Voronin (1) (2)
  Yu. M. Laevsky (1) (2)
  
  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia
  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1995-4247

文摘

In this paper, the stability of some splitting schemes approximating heat flux equations obtained by a mixed finite element method is investigated. For a two-dimensional problem, the splitting scheme is based on an alternating direction method, and for a three-dimensional problem, on the Douglas—Gunn scheme.