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International Conference on Large-Scale Scientific Computing

LSSC 2005: Large-Scale Scientific Computing pp 76–83Cite as

Discretization of Integro-Differential Equations Modeling Dynamic Fractional Order Viscoelasticity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3743))

Abstract

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integro-differential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equation of motion. These are then used to prove a priori error estimates. A numerical experiment is included.

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References

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Author information

Authors and Affiliations

  1. Dept. of Appl. Mech., Chalmers Univ. of Technology, SE–412 96, Göteborg, Sweden

    K. Adolfsson & M. Enelund

  2. Dept. of Mathematics, Chalmers Univ. of Technology, SE–412 96, Göteborg, Sweden

    S. Larsson

  3. Dept. of Mathematics, Technical University of Gabrovo, 5300, Gabrovo, Bulgaria

    M. Racheva

Authors
  1. K. Adolfsson
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  2. M. Enelund
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  3. S. Larsson
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  4. M. Racheva
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2006 Springer-Verlag Berlin Heidelberg

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Adolfsson, K., Enelund, M., Larsson, S., Racheva, M. (2006). Discretization of Integro-Differential Equations Modeling Dynamic Fractional Order Viscoelasticity. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_7

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  • DOI: https://doi.org/10.1007/11666806_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31994-8

  • Online ISBN: 978-3-540-31995-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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