dc.contributor.author |
Appadu, A. Rao
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|
dc.contributor.author |
Djoko, J.K. (Jules Kamdem)
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dc.contributor.author |
Gidey, H.H.
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dc.date.accessioned |
2017-11-20T07:05:43Z |
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dc.date.issued |
2017-12 |
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dc.description.abstract |
In this work, we analyze four finite volume methods for the nonlinear convective Cahn–Hilliard equation with specified initial condition and periodic boundary conditions. The methods used are: implicit one-level, explicit one-level, implicit multilevel and explicit multilevel finite volume methods. The existence and uniqueness of solution, convergence and stability of the finite volume solutions are proved. We compute L2- error and rate of convergence for all methods. We then compare the multilevel methods with the one-level methods by means of stability and CPU time. It is shown that the multilevel finite volume method is faster than the one-level method. |
en_ZA |
dc.description.department |
Mathematics and Applied Mathematics |
en_ZA |
dc.description.embargo |
2018-12-01 |
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dc.description.librarian |
hj2017 |
en_ZA |
dc.description.sponsorship |
A.R. Appadu is grateful to the DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences and the National Research Foundation of South Africa Grant No. 95864 for funding. J. K. Djoko is funded through the incentive fund N00 401 Project 85796. H. H. Gidey is grateful to the University of Pretoria, African Institute for Mathematical Sciences (AIMS)-South Africa and Aksum University (Ethiopia) for their financial support for his Ph.D. studies. |
en_ZA |
dc.description.uri |
https://link.springer.com/journal/13370 |
en_ZA |
dc.identifier.citation |
Appadu, A.R., Djoko, J.K. & Gidey, H.H. A priori analysis of multilevel finite volume approximation of 1D convective Cahn–Hilliard equation. Afrika Matematika (2017) 28: 1193-1233. https://doi.org/10.1007/s13370-017-0512-x. |
en_ZA |
dc.identifier.issn |
1012-9405 (print) |
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dc.identifier.issn |
2190-7668 (online) |
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dc.identifier.other |
10.1007/s13370-017-0512-x |
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dc.identifier.uri |
http://hdl.handle.net/2263/63204 |
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dc.language.iso |
en |
en_ZA |
dc.publisher |
Springer |
en_ZA |
dc.rights |
© African Mathematical Union and Springer-Verlag GmbH Deutschland 2017. The original publication is available at : https://link.springer.com/journal/13370. |
en_ZA |
dc.subject |
Cahn–Hilliard (CH) equation |
en_ZA |
dc.subject |
Convective Cahn–Hilliard |
en_ZA |
dc.subject |
Multilevel |
en_ZA |
dc.subject |
Finite volume |
en_ZA |
dc.subject |
Convergence |
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dc.subject |
Stability |
en_ZA |
dc.subject |
Uniqueness |
en_ZA |
dc.subject |
Existence |
en_ZA |
dc.title |
A priori analysis of multilevel finite volume approximation of 1D convective Cahn–Hilliard equation |
en_ZA |
dc.type |
Postprint Article |
en_ZA |