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Upper Bound of the Constant in Strengthened C.B.S. Inequality for Systems of Linear Partial Differential Equations

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Abstract

The constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is the framework of finite element approximations of systems of partial differential equations. We consider an approximation of general systems of linear partial differential equations in R 3. Concerning a multilevel convergence rate corresponding to nested general tetrahedral meshes of size h and 2h, we give an estimate of this constant for general three-dimensional cases.

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Authors and Affiliations

  1. Université Hassan 1er, Faculté des sciences juridiques, économiques et sociales, Settat, B.P. 784, Settat, Maroc

    B. Achchab

  2. LERMA, Ecole Mohammadia d'Ingénieurs, Avenue Ibn Sina, B.P. 765, Rabat-Agdal, Maroc

    B. Achchab, S. Achchab & A. Souissi

  3. Department of Mathematics, University of Nijmegen, Postbus 9010 NL-, 6500 GL, Nijmegen, The Netherlands

    O. Axelsson

  4. Université Mohammed V-Agdal, Faculté des sciences, Département de Mathématiques et d'Informatique, Avenue Ibn Battouta, B.P. 1014, Rabat, Maroc

    A. Souissi

Authors
  1. B. Achchab
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  2. S. Achchab
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  3. O. Axelsson
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  4. A. Souissi
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Achchab, B., Achchab, S., Axelsson, O. et al. Upper Bound of the Constant in Strengthened C.B.S. Inequality for Systems of Linear Partial Differential Equations. Numerical Algorithms 32, 185–191 (2003). https://doi.org/10.1023/A:1024058625449

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