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Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem
Journal
SIAM Journal on Scientific Computing
ISSN
1095-7197
Date Issued
2020
Author(s)
Verónica Anaya
Zoa de Wijn
Bryan Gómez-Vargas
David Mora
Ricardo Ruiz-Baier
DOI
10.1137/19M1268343
Abstract
In this paper we introduce a new formulation for the stationary poroelasticity equations
written using the rotation vector and the total fluid-solid pressure as additional unknowns, and
we also write an extension to the elasticity-poroelasticity problem. The transmission conditions are
imposed naturally in the weak formulation, and the analysis of the effective governing equations is
conducted by an application of Fredholm's alternative. We also propose a monolithically coupled
mixed finite element method for the numerical solution of the problem. Its convergence properties
are rigorously derived and subsequently confirmed by a set of computational tests that include
applications to subsurface flow in reservoirs as well as to dentistry-oriented problems.
written using the rotation vector and the total fluid-solid pressure as additional unknowns, and
we also write an extension to the elasticity-poroelasticity problem. The transmission conditions are
imposed naturally in the weak formulation, and the analysis of the effective governing equations is
conducted by an application of Fredholm's alternative. We also propose a monolithically coupled
mixed finite element method for the numerical solution of the problem. Its convergence properties
are rigorously derived and subsequently confirmed by a set of computational tests that include
applications to subsurface flow in reservoirs as well as to dentistry-oriented problems.
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