Abstract
We focus on a three-field (displacement-velocity-pressure) stabilized mixed method for poroelasticity based on piecewise trilinear (Q1), lowest order Raviart-Thomas (RT0), and piecewise constant (P0) approximations for displacement, Darcy’s velocity and fluid pore pressure, respectively. Since the selected discrete spaces do not intrinsically satisfy the inf-sup condition in the undrained/incompressible limit, we propose a stabilization strategy based on local pressure jumps. Then, we focus on the efficient solution of the stabilized formulation by a block preconditioned Krylov method. Robustness and efficiency of the proposed approach are demonstrated in two sets of numerical experiments.
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Acknowledgements
Funding was provided by TOTAL S.A. through the FC-MAELSTROM project. Portions of this work were performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07-NA27344.
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Ferronato, M., Frigo, M., Castelletto, N., White, J.A. (2021). Efficient Solvers for a Stabilized Three-Field Mixed Formulation of 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_41
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DOI: https://doi.org/10.1007/978-3-030-55874-1_41
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