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Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics

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Abstract

In this paper, we consider an iterative coupling scheme for solving a fully discretized Biot system based on the fixed-stress split coupling algorithm. Specifically, we derive a priori error estimates for quantifying the error between the solution obtained at any iterate and the true solution. Our approach is based on studying the equations satisfied by the difference of iterates and utilizing a Banach contraction argument to show that the corresponding scheme is a fixed point iteration. Obtained contraction results are then used to derive theoretical convergence error estimates for the single rate iterative coupling scheme. We compare our numerical computations against the theoretically derived contraction estimates and show a good agreement with theory.

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Acknowledgements

TA is funded by Saudi Aramco. We thank Paulo Zunino and Ivan Yotov for helpful discussions. KK would like to acknowledge the support of Toppforsk project ThemSes funded by Norwegian Research Council. The authors would like to acknowledge the CSM Industrial Affiliates program, DOE grant ER25617, and ConocoPhillips grant UTA10-000444. Moreover, we thank Gurpreet Singh for his help and support with IPARS.

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Authors and Affiliations

  1. Center for Subsurface Modeling, ICES, UT-Austin, Austin, TX, 78712, USA

    T. Almani & M. F. Wheeler

  2. Mathematics Institute, University of Bergen, Bergen, Norway

    K. Kumar

  3. Saudi Arabian Oil Company (Aramco), Dhahran, Saudi Arabia

    T. Almani

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  1. T. Almani
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  2. K. Kumar
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Correspondence to T. Almani.

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Almani, T., Kumar, K. & Wheeler, M.F. Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput Geosci 21, 1157–1172 (2017). https://doi.org/10.1007/s10596-017-9691-7

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