Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:440

Article

Keita, Sana^1,2  Beljadid, Abdelaziz^1,2  Bourgault, Yves² 

[1] Mohammed VI Polytech Univ, Int Water Res Inst, Ben Guerir, Morocco

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

关键词: Fourth-order equation;    Mixed finite element;    Second-order time-accuracy;    Conservative scheme;    Positivity preserving;   

DOI  :  10.1016/j.jcp.2021.110427

来源: Elsevier

【 摘 要 】

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 [10]. 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free