Analysis of multilevel finite volume approximation of 2D convective Cahn–Hilliard equation
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Date
Authors
Appadu, A. Rao
Djoko, J.K. (Jules Kamdem)
Gidey, H.H.
Lubuma, Jean M.-S.
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
In this work, four finite volume methods have been constructed to solve the
2D convective Cahn–Hilliard equation with specified initial condition and periodic
boundary conditions. We prove existence and uniqueness of solutions. The stability
and convergence analysis of the numerical methods have been discussed thoroughly.
The nonlinear terms are approximated by a linear expression based on Mickens’ rule
(Mickens, Nonstandard finite difference models of differential equations. World Scientific,
Singapore, 1994) of nonlocal approximations of nonlinear terms. Numerical
experiments for a test problem have been carried out to test all methods.
Description
Keywords
2D convective Cahn–Hilliard equation, Existence of solution, Uniqueness, Stability, Convergence, Finite volume, Multilevel
Sustainable Development Goals
Citation
Appadu, A.R., Djoko, J.K., Gidey, H.H. & Lubuma, J.M.S. Analysis of multilevel finite volume approximation of 2D convective Cahn–Hilliard equation. Japan Journal of Industrial and Applied Mathematics (2017) 34: 253-304. doi:10.1007/s13160-017-0239-y.