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A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis

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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 120))

Abstract

In this essay the rigorous application of the method of vertical lines, i.e. performing the successive steps of spatial and temporal discretization is investigated for dynamical and quasi-statical systems. A particular focus lies in the field of solid mechanics where constitutive models of evolutionary-type are of basic interest. Various coupled systems, i.e. thermo-mechanical, electro-thermal or electro-thermo-mechanical coupled problems are investigated in view of the structure of their resulting equations, commonly, leading to systems of ordinary differential equations or systems of differential-algebraic equations after the spatial discretization step. For the case of a thermo-mechanical and an electro-thermal problem stiffly accurate diagonally-implicit Runge-Kutta methods are applied.

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Authors and Affiliations

  1. Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2a, 38678, Clausthal-Zellerfeld, Germany

    Stefan Hartmann & Steffen Rothe

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  1. Stefan Hartmann
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  2. Steffen Rothe
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Correspondence to Stefan Hartmann .

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Editors and Affiliations

  1. , Department of Mathematics, University of Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Rainer Ansorge

  2. , Department of Aerospace Engineering, Delft University of Technology, Delft, 2600, Netherlands

    Hester Bijl

  3. , Department of Mathematics and Natural Sc, University of Kassel, Heinrich-Plett-Str. 40, Kassel, 34132, Germany

    Andreas Meister

  4. Institute for Computational Mathematics, Technical University of Braunschweig, Pockelstr. 14, Braunschweig, 38106, Germany

    Thomas Sonar

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Hartmann, S., Rothe, S. (2013). A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

  • Online ISBN: 978-3-642-33221-0

  • eBook Packages: EngineeringEngineering (R0)

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