Undergraduate Thesis of Ricardo E. Oyarzua
Career | Mathematical Civil Engineering, Universidad de Concepción | |
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Enrollment Year | 1998 | |
Senior Year | 2006 | |
Thesis Title | A 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 Date | 2005, August 24 | |
Thesis Defense Date | 2007, January 10 | |
Professional Monitoring | As of March 2007, PhD studies in Applied Sciences with mention in Mathematical Engineering at the Universidad de Concepción. | |
PDF Tesis | Download Thesis PDF | |
ISI Publications from the ThesisGabriel N. GATICA, Salim MEDDAHI, Ricardo OYARZúA: 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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