@article{31e2bfcf65af4e5cbb2e31656990d9a4,
title = "Analysis of multilevel finite volume approximation of 2D convective Cahn–Hilliard equation",
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{\textquoteright} 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.",
author = "Appadu, {A. R.} and Djoko, {J. K.} and Gidey, {H. H.} and Lubuma, {J. M.S.}",
note = "Funding Information: A.R. Appadu is grateful to the South African DST/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences of the University of Pretoria and to the National Research Foundation of South African Grant Number 95864. 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, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) and Aksum University (Ethiopia) for their financial support for his PhD studies.We thank the referee for many remarks that have led to some improvements in the text. Publisher Copyright: {\textcopyright} 2017, The JJIAM Publishing Committee and Springer Japan.",
year = "2017",
month = apr,
day = "1",
doi = "10.1007/s13160-017-0239-y",
language = "English",
volume = "34",
pages = "253--304",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",
}