Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 405, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2021.113953
Keywords
Poroelasticity; Hydraulic fracturing; Contact; Elliptic-parabolic problem; Well-posedness analysis; Rothes MOL
Categories
Funding
- Austrian Science Fund (FWF) [P26147-N26: PION]
- European Research Council (ERC) under the European Union [668998 OCLOC]
- Russian Foundation for Basic Research (RFBR) [18-29-10007]
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A new class of unilateral variational models is introduced and studied in the field of poroelasticity. The fully coupled poroelastic system under the unilateral constraint is analyzed, and the well-posedness of the corresponding variational inequality is established. A non-linear complementarity problem formulation is given for solving the non-penetration conditions, which provides an effective numerical solution strategy.
A new class of unilateral variational models appearing in the theory of poroelasticity is introduced and studied. A poroelastic medium consists of solid phase and pores saturated with a Newtonian fluid. The medium contains a fluid-driven crack, which is subjected to non-penetration between the opposite crack faces. The fully coupled poroelastic system includes elliptic-parabolic governing equations under the unilateral constraint. Well-posedness of the corresponding variational inequality is established based on the Rothe semi-discretization in time, after subsequent passing time step to zero. The NLCP-formulation of non-penetration conditions is given which is useful for a semi-smooth Newton solution strategy. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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