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Undergraduate Thesis of Ricardo E. Oyarzua

Oyarzua, Ricardo E.CareerMathematical Civil Engineering, Universidad de Concepción
Enrollment Year1998
Senior Year2006
Thesis TitleA Mixed Finite Element Method For Coupling Fluids With Porous Media

Thesis Summary:

In this work we consider a porous medium inserted in a fluid, and we present a method of mixed finite elements according to the corresponding coupled problem. The conditions of transmission at the interface of both domains are given by: balance of normal forces, mass conservation, and Beavers-Joseph-Saffman's law, which induces the introduction of the pressure trace in the porous medium as a Lagrange multiplier. The finite element subspaces used in the discrete scheme are the Bernardi-Raugel and Raviart-Thomas elements for velocities, constant by length for the pressure, and continuous and linear elements by length for the Lagrange multiplier. In addition, we give a reliable posterior error estimator for the Galerkin scheme. This report is organized as follows. In Chapter 1 we introduce the problem of interest boundary values ​​and define the finite elements of Bernardi-Raugel, which are used to approximate the velocity in the fluid. In Chapter 2 we present the continuous and discrete schemes and show that both are well proposed. In Chapter 3 we give some numerical results showing the good behavior of the method. In Chapter 4 a reliable a posteriori error estimator is deduced and, finally, in Chapter 5 numerical results are given that illustrate its reliability.

Thesis Director(s) Gabriel N. Gatica
Thesis Project Approval Date2005, August 24
Thesis Defense Date2007, January 10
Professional MonitoringAs of March 2007, PhD studies in Applied Sciences with mention in Mathematical Engineering at the Universidad de Concepción.
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ISI Publications from the Thesis

Gabriel N. GATICA, Salim MEDDAHI, Ricardo OYARZUA: A conforming mixed finite-element method for the coupling of fluid flow with porous media flow. IMA Journal of Numerical Analysis, vol. 29, 1, pp. 86-108, (2009)

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