An exactly divergence-free finite element method for non-isothermal flow problems
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Qin, Tong
issued: 2013-09-03T17:13:16Z
issued: 2013
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: In this thesis the exactly divergence-free finite element method developed by Cockburn, Scheotzau and Kanschat in [13] and [14] is studied. This method is first reviewed in the context of Stokes problem. An interior penalty discontinuous Galerkin approach is formulated and analysed in the unified framework established in [13], [14] and [37]. Then we extend the method to non-isothermal flow problems, in particular, to a generalised Boussinesq equation. Following the work by Ricardo, Scheotzau and Qin in [34], the method is formulated and the numerical analysis is reviewed. Numerical examples are implemented and presented, which verify the theoretical error estimates and the exactly divergence-free property.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/45013
note: An Exactly Divergence-free Finite Element Method forNon-isothermal Flow ProblemsbyTong QinB.S. University of Science and Technology of China, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Mathematics)The University of British Columbia(Vancouver)August 2013c? Tong Qin, 2013AbstractIn this thesis the exactly divergence-free finite element method developed in [13] and [14]is studied. This method is first reviewed in the context of Stokes problem. An interiorpenalty discontinuous Galerkin approach is formulated and analysed in the framework of[13], [14] and [37]. Then we extend the method to non-isothermal flow problems, in partic-ular, to a generalised Boussinesq equation. Following [34], the method is formulated andthe numerical analysis is reviewed. Numerical examples are implemented and presented,which verify the theoretical error estimates and the exactly divergence-free property.iiPrefaceIn this dissertation, the theoretical analysis in Chapter 1 is a review and synthesis ofthe work in [13], [14] and [37]. And the numerical experiments in Section 2.5 are carriedout independently by the author T. Qin. The Chapter 2 is a summary and review of thepaper [34] which is a collaboration with R. Oyarzu?a and D. Scho?tzau. The formulationof the method is an extension of the work in [14]. The theoretical analysis is attributedto Oyarzu?a and Scho?tzau. The author formulated the fixed-point iteration in Section 3.7and extended the code to the generalized Boussinesq equation in Section 3.8. All thenumerical experiments in this thesis are conducted with the deal.II finite element library[5]. A journal paper related with the work in Chapter 2 has been submitted to andaccepted by the IMA Journal of Applied Mathematics.iiiContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . …
has type: Thesis/Dissertation
date issued: 2013-11
is shown at: 10.14288/1.0074239
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/45013