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A New Approach to Constructing Splitting Schemes in Mixed FEM for Heat Transfer: A Priori Estimates

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Finite Difference Methods,Theory and Applications (FDM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9045))

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Abstract

A priori estimates for a new approach to constructing vector splitting schemes in mixed FEM for heat transfer problems are presented. Heat transfer problem is considered in the mixed weak formulation approximated by Raviart-Thomas finite elements of lowest order on rectangular meshes. The main idea of the considered approach is to develop splitting schemes for the heat flux using well-known splitting scheme for the scalar function of flux divergence. Based on flux decomposition into discrete divergence-free and potential (orthogonal) components, a priori estimates for 2D and 3D vector splitting schemes are presented. Special attention is given to the additional smoothness requirements imposed on the initial heat flux. The role of these requirements is illustrated by several numerical examples.

This work was financially supported by RFBR grant No. 13-01-00019.

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References

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, 630090, Novosibirsk, Russia

    Kirill Voronin & Yuri Laevsky

Authors
  1. Kirill Voronin
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  2. Yuri Laevsky
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Corresponding author

Correspondence to Kirill Voronin .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Voronin, K., Laevsky, Y. (2015). A New Approach to Constructing Splitting Schemes in Mixed FEM for Heat Transfer: A Priori Estimates. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_47

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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