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Stokes-Biot Modeling of Flow in Fractured Poroelastic Media

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Monday, October 23, 2017
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12:00 pm - 1:00 pm
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Ivan Yotov, Professor, University of Pittsburgh, Department of Mathematics

We study mathematical models and their finite element approximations
for solving the coupled problem arising in the interaction between
fluid in a poroelastic material and fluid in a fracture. The fluid
flow in the fracture is governed by the Stokes/Brinkman equations,
while the poroelastic material is modeled using the Biot system. We
present several approaches to impose the continuity of normal flux,
including an interior penalty method and a Lagrange multiplier
method. A dimensionally reduced fracture model based on averaging
the equations over the cross-sections will also be presented.
Stability, accuracy, and robustness of the methods will be discussed.