Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations
Abstract
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem and then an optimization problem to satisfy the desired physical properties of the solution such as conservation of mass, positivity (non-negativity) of solution and dissipation of energy. Furthermore, we show existence and uniqueness of the solution to the optimization problem and we prove that the methods converge to the truncation schemes \cite{Berger1975}. We also propose new conservative truncation methods for high-order parabolic equations. A numerical convergence study is performed and a series of numerical tests are presented to show and compare the efficiency and robustness of the different schemes.
Keywords
Cite
@article{arxiv.2010.11913,
title = {Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations},
author = {Sana Keita and Abdelaziz Beljadid and Yves Bourgault},
journal= {arXiv preprint arXiv:2010.11913},
year = {2021}
}