Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations
Thesis (PhD)--University of Pretoria, 2014.
Saved in:
| Other Authors: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
University of Pretoria
2015
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613437674127360 |
|---|---|
| access_status_str | Open Access |
| author2 | Djoko, J.K. (Jules Kamdem) |
| author_browse | Djoko, J.K. (Jules Kamdem) |
| author_facet | Djoko, J.K. (Jules Kamdem) |
| collection | Thesis |
| dc_rights_str_mv | © 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD)--University of Pretoria, 2014. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/43183 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:08.220Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/43183 Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations Djoko, J.K. (Jules Kamdem) mbehoumohe@yahoo.fr Mohamed, Mbehou UCTD Thesis (PhD)--University of Pretoria, 2014. This thesis is divided in three main chapters devoted to the study of finite element approximations of fluid flows with special nonlinearities coming from boundary con- ditions. In Chapter 1, we consider the finite element approximations of steady Navier-Stokes and Stokes equations driven by threshold slip boundary conditions. After re-writing the problems in the form of variational inequalities, a fixed point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge respectively to the solutions of each continuous problem. Finally, Uzawa’s algorithm is formulated and convergence of the procedure is shown, and numerical validation tests are achieved. Chapter 2 is concerned with the finite element approximation for the stationary power law Stokes equations driven by slip boundary conditions of “friction type”. It is shown that by applying a variant of Babuska-Brezzi’s theory for mixed problems, convergence of the finite element approximation formulated is achieved with classi- cal assumptions on the regularity of the weak solution. Solution algorithm for the mixed variational problem is presented and analyzed in details. Finally, numerical simulations that validate the theoretical findings are exhibited. In Chapter 3, we are dealing with the study of the stability for all positive time of Crank-Nicolson scheme for the two-dimensional Navier-Stokes equation driven by slip boundary conditions of “friction type”. We discretize these equations in time using the Crank-Nicolson scheme and in space using finite element approximation. We prove that the numerical scheme is stable in L2 and H1-norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition. lk2014 Mathematics and Applied Mathematics PhD Unrestricted 2015-01-19T12:11:12Z 2015-01-19T12:11:12Z 2014/12/12 2014 Thesis Mohamed, M 2014, Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations, PhD Thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/43183> D14/9/34 http://hdl.handle.net/2263/43183 en © 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations |
| title | Finite element approximations for fluid
flows governed by nonlinear slip boundary
conditions of friction type: from theory to
computations |
| title_full | Finite element approximations for fluid
flows governed by nonlinear slip boundary
conditions of friction type: from theory to
computations |
| title_fullStr | Finite element approximations for fluid
flows governed by nonlinear slip boundary
conditions of friction type: from theory to
computations |
| title_full_unstemmed | Finite element approximations for fluid
flows governed by nonlinear slip boundary
conditions of friction type: from theory to
computations |
| title_short | Finite element approximations for fluid
flows governed by nonlinear slip boundary
conditions of friction type: from theory to
computations |
| title_sort | finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type from theory to computations |
| topic | UCTD |
| url | http://hdl.handle.net/2263/43183 |