Conservative stable discretizations and parameter-robust preconditioners for three-field formulation of Biot's consolidation model

CCMA PDEs and Numerical Methods Seminar Series

Meeting Details

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Speaker: Qingguo Hong, Penn State University

Abstract: This talk is devoted to the stability analysis of a classical three-field formulation of Biot’s consolidation model where the unknown variables are the displacements, fluid flux (Darcy velocity), and pore pressure. Specific parameter-dependent norms provide the key in establishing the full parameter- robust inf-sup stability of the continuous problem. Therefore, stability results presented here are uniform not only with respect to the Lam ́e parameter λ, but also with respect to all the other model parameters. This allows for the construction of a uniform block diagonal preconditioner within the framework of operator preconditioning. Stable discretizations that meet the required conditions for full robustness and guarantee mass conservation, both locally and globally, are discussed and corresponding optimal error estimates proven.

Room Reservation Information

Room Number: 315 McAllister

Date: 03/28/2018

Time: 10:00am - 12:00pm