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Analysis of the CBS Constant for Quadratic Finite Elements

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Numerical Methods and Applications (NMA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6046))

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Abstract

We study the behavior of the CBS constant as a quality measure for hierarchical two-level splittings of quadratic FEM stiffness matrices. The article is written in the spirit of [3] where the focus is on the robustness with respect to mesh and coefficient anisotropy. The considered splittings are: Differences and Aggregates (DA); First Reduce (FR); and hierarchical P-decomposition (P). The presented results show sufficient conditions for the existence of optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners.

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References

  1. Axelsson, O.: Stabilization of Algebraic Multilevel Iteration method; additive methods. Numerical Algorithms, 23–47 (1999)

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  2. Blaheta, R., Margenov, S., Neytcheva, M.: Uniform Estimate of the Constant in the Strengthened CBS inequality for Anisotropic Non-conforming FEM systems. Numerical Linear Algebra and Applications 11(4), 309–326 (2004)

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  3. Kraus, J., Margenov, S.: Robust Algebraic Multilevel Methods and Algorithms. De Gruyter, Germany (2009)

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  4. Maitre, J.F., Musy, S.: The Contraction Number of a Class of Two-level Methods; An Exact Evaluation for Some Finite Element Subspaces and Model Problems. Lect. Notes Math., vol. 960, pp. 535–544 (1982)

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 25A, 1113, Sofia, Bulgaria

    Maria Lymbery & Svetozar Margenov

Authors
  1. Ivan Georgiev
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  2. Maria Lymbery
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  3. Svetozar Margenov
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Editor information

Editors and Affiliations

  1. Institute of Computer and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Faculty of Mathematics and Informatics, Department Numerical Methods and Algorithms, University of Sofia "St. Kliment Ohridski",, blvd. James Bourchier 5, 1164, Sofia, Bulgaria

    Stefka Dimova

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Bonchev St.,Bl.8, 1113, Sofia, Bulgaria

    Natalia Kolkovska

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Georgiev, I., Lymbery, M., Margenov, S. (2011). Analysis of the CBS Constant for Quadratic Finite Elements. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_49

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  • DOI: https://doi.org/10.1007/978-3-642-18466-6_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18465-9

  • Online ISBN: 978-3-642-18466-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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