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Iterative Coupling for Fully Dynamic Poroelasticity

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Numerical Mathematics and Advanced Applications ENUMATH 2019

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 139))

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Abstract

We present an iterative coupling scheme for the numerical approximation of the mixed hyperbolic-parabolic system of fully dynamic poroelasticity. We prove its convergence in the Banach space setting for an abstract semi-discretization in time that allows the application of the family of diagonally implicit Runge–Kutta methods. Recasting the semi-discrete solution as the minimizer of a properly defined energy functional, the proof of convergence uses its alternating minimization. The scheme is closely related to the undrained split for the quasi-static Biot system.

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Acknowledgements

This work was supported by the German Academic Exchange Service (DAAD) under the grant ID 57458510 and by the Research Council of Norway (RCN) under the grant ID 294716.

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Authors and Affiliations

  1. Helmut Schmidt University, Hamburg, Germany

    Markus Bause

  2. University of Bergen, Bergen, Norway

    Jakub W. Both & Florin A. Radu

Authors
  1. Markus Bause
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  2. Jakub W. Both
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  3. Florin A. Radu
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Correspondence to Markus Bause .

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Editors and Affiliations

  1. DIAM, Delft University of Technology, Delft, The Netherlands

    Fred J. Vermolen

  2. DIAM, Delft University of Technology, Delft, The Netherlands

    Cornelis Vuik

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Bause, M., Both, J.W., Radu, F.A. (2021). Iterative Coupling for Fully Dynamic Poroelasticity. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_10

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