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Applied Mathematics Colloquium: Dr Ivan Yotov

University of Pittsburgh

Friday, April 1, 2022
2:00 PM – 3:00 PM
Title: Stokes-Biot modeling of fluid-poroelastic structure interaction 

Abstract: We study mathematical models and their finite element approximations 
for solving the coupled problem arising in the interaction between a 
free fluid and a fluid in a poroelastic material. Applications of 
interest include flows in fractured poroelastic media, coupling of 
surface and subsurface flows, and arterial flows.  The free fluid flow 
is governed by the Navier-Stokes or Stokes/Brinkman equations, while 
the poroelastic material is modeled using the Biot system of 
poroelasticity. The two regions are coupled via dynamic and kinematic 
interface conditions, including balance of forces, continuity of 
normal velocity, and no-slip or slip with friction tangential velocity 
condition. Well posedness of the weak formulations is established 
using techniques from semigroup theory for evolution PDEs with 
monotone operators. Mixed finite element methods are employed for the 
numerical approximation. Solvability, stability, and accuracy of the 
methods are analyzed with the use of suitable discrete inf-sup 
conditions. Numerical results will be presented to illustrate the 
performance of the methods, including their flexibility and robustness 
for several applications of interest. 
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