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Process Machine Interactions pp 53–77Cite as

Adaptive Finite Elements and Mathematical Optimization Methods

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Part of the book series: Lecture Notes in Production Engineering ((LNPE))

Abstract

This chapter focuses on the topics of mathematical research in the priority program and on the application of the results to engineering problems. First, a posteriori estimates and adaptive methods based on them are presented for contact problems. In detail, frictional contact problems using a linear elastic material law, which are discretized by a dual-dual method, are considered. Using a different approach, adaptive methods are derived for elasto-plasticity with contact and friction. Then results for contact problems involving inertial effects are introduced. Second, parameter identification and inverse problems are considered. After an introduction into the general problem of setting and solution techniques, the balancing of a rotating system is discussed as a prototypical industrial application.

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Author information

Authors and Affiliations

  1. Institute for Applied Mathematics, Leibniz Universität Hannover, Hannover, Germany

    M. Andres, C. Brandt, C. Carstensen, P. Maaß, J. Niebsch, A. Rademacher, R. Ramlau, A. Schröder, E. -P. Stephan & S. Wiedemann

  2. Faculty of Mathematics (LS X), Technische Universität Dortmund, Dortmund, Germany

    H. Blum

Authors
  1. M. Andres
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  2. H. Blum
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  3. C. Brandt
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  4. C. Carstensen
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  5. P. Maaß
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  6. J. Niebsch
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  7. A. Rademacher
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  8. R. Ramlau
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  9. A. Schröder
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  10. E. -P. Stephan
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  11. S. Wiedemann
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Editor information

Editors and Affiliations

  1. , Institut for Production Engineering, Leibniz Universität Hannover, An der Universität 2, Garbsen, 30823, Germany

    Berend Denkena

  2. Deutsche Forschungsgemeinschaft, Kennedyallee 40, Bonn, 53175, Germany

    Ferdinand Hollmann

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Andres, M. et al. (2013). Adaptive Finite Elements and Mathematical Optimization Methods. In: Denkena, B., Hollmann, F. (eds) Process Machine Interactions. Lecture Notes in Production Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32448-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-32448-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32447-5

  • Online ISBN: 978-3-642-32448-2

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