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Volume 15, Issue 1
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation

Xiaowei Chen, Xu Qian & Songhe Song

Adv. Appl. Math. Mech., 15 (2023), pp. 159-181.

Published online: 2022-10

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  • 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.

  • AMS Subject Headings

65N06, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-159, author = {Chen , XiaoweiQian , Xu and Song , Songhe}, title = {Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0325}, url = {http://global-sci.org/intro/article_detail/aamm/21130.html} }
TY - JOUR T1 - Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation AU - Chen , Xiaowei AU - Qian , Xu AU - Song , Songhe JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 159 EP - 181 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0325 UR - https://global-sci.org/intro/article_detail/aamm/21130.html KW - Maximum-principle-preserving, mass-conserving scheme, the conservative Allen-Cahn equation. AB -

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.

Xiaowei Chen, Xu Qian & Songhe Song. (2022). Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation. Advances in Applied Mathematics and Mechanics. 15 (1). 159-181. doi:10.4208/aamm.OA-2021-0325
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