Graduate Studies
First Advisor
George Avalos
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics
Date of this Version
8-2024
Document Type
Dissertation
Citation
A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy
Major: Mathmatics
Under the supervision of Professor George Avalos
Lincoln, Nebraska, August 2024
Abstract
The coupling of a porous medium modeled by the Biot equations and a fluid has many biological applications. There are numerous ways by which to model the fluid and to couple the porous medium with the fluid. This particular model couples the Biot equations to Stokes flow along the boundary, through the Beavers-Joseph-Saffman conditions. We address semigroup well-posedness of the system via an inf-sup approach, which along the way requires consideration of a related but uncoupled static Biot system. We also present the results of finite element analysis on both the uncoupled Biot system and the coupled system.
Advisor: Sara McKnight
Recommended Citation
McKnight, Sara, "Semigroup Well-posedness and Finite Element Analysis of a Biot-Stokes Interactive System" (2024). Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–. 149.
https://digitalcommons.unl.edu/dissunl/149
Comments
Copyright 2024, Sara McKnight. Used by permission