Analysis and Implementation of Some Stabilized Finite Element Methods Applied to Fluid Mechanics

Cáceres-Valenzuela, Ernesto David

Full Metadata

Overview

Year:: 2022
Contributor:: Cáceres-Valenzuela, Ernesto David (creator); Guzmán, Johnny (Advisor); Shu, Chi-Wang (Reader); Barrenechea, Gabriel (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Finite element method
Extent:: xvi, 147 p.

Files

Description

Abstract:: In this dissertation we propose, analyze and computationally implement finite element models to two different two-dimensional saddle point systems of partial differential equations with boundary conditions that arise from the well known Navier-Stokes equations. In both cases, we formulate the continuous model that gives the solution to the system of partial differential equations under consideration in the form of a mixed variational formulation, and then consider a discrete, finite-dimensional version of such model, which aims to approximate the solution of it. Next, we establish the stability of the discrete model and perform an error analysis, where we make explicit the rate at which the approximate solution converges to the continuous one with respect to different norms, such as the L^2, H^1 and L-infinity ones. Additionally, numerical experiments that support the theoretical findings are presented and some key details about the implementation of each method are discussed.
Notes:: Thesis (Ph. D.)--Brown University, 2022

Content

Citation

Cáceres-Valenzuela, Ernesto David, "Analysis and Implementation of Some Stabilized Finite Element Methods Applied to Fluid Mechanics" (2022). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:t5g9xz6p/

Relations

Collection:

Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.
...