Year: 2023
Author: Xiaowei Chen, Xu Qian, Songhe Song
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 159–181
Abstract
We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is verified by several numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0325
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 159–181
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Maximum-principle-preserving mass-conserving scheme the conservative Allen-Cahn equation.
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