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Modeling, Simulation and Optimization for Science and Technology pp 83–92Cite as

Numerical Analysis and Simulation of the Dynamics of Mountain Glaciers

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 34))

Abstract

In this chapter, we analyze and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solutions are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice, which describes the time evolution of a glacier. The accumulation due to snow precipitation and melting are accounted for in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a two-grids method. As an illustration, we simulate the evolution of Aletsch glacier, Switzerland, over the 21st century by using realistic climatic conditions.

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Acknowledgments

The first author was supported by the Deutsche Forschungsgemeinschaft (project KL 1806 5-1).

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Authors and Affiliations

  1. Institut für Mathematik, Freie Universität Berlin, 14195, Berlin, Germany

    Guillaume Jouvet

  2. Institut d’Analyse et Calcul Scientifique, EPFL, 1015, Lausanne, Switzerland

    Jacques Rappaz

Authors
  1. Guillaume Jouvet
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  2. Jacques Rappaz
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Corresponding author

Correspondence to Guillaume Jouvet .

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Editors and Affiliations

  1. College of Technology, University of Houston, Houston, Texas, USA

    William Fitzgibbon

  2. Department of Mathematics, University of Houston, Houston, Texas, USA

    Yuri A. Kuznetsov

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  4. Laboratoire Jacques-Louis Lions, University of Paris VI, Paris, France

    Olivier Pironneau

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Jouvet, G., Rappaz, J. (2014). Numerical Analysis and Simulation of the Dynamics of Mountain Glaciers. In: Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Pironneau, O. (eds) Modeling, Simulation and Optimization for Science and Technology. Computational Methods in Applied Sciences, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9054-3_5

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  • DOI: https://doi.org/10.1007/978-94-017-9054-3_5

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9053-6

  • Online ISBN: 978-94-017-9054-3

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