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Volume 16, Issue 3
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations

Congying Li, Liang Tang & Jie Zhou

Adv. Appl. Math. Mech., 16 (2024), pp. 667-691.

Published online: 2024-02

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  • Abstract

In this paper, we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations. Stabilized semi-implicit schemes are used for temporal discretization, and the finite element method is used for spatial discretization. It is shown that by adding a single linear term that is of the same order with the truncation error in time, the proposed methods are all unconditionally energy stable. Error estimates for the two schemes are also established. Numerical examples are presented to confirm the accuracy, efficiency and stability of the proposed methods.

  • AMS Subject Headings

65N15, 65N30, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-667, author = {Li , CongyingTang , Liang and Zhou , Jie}, title = {Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {667--691}, abstract = {

In this paper, we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations. Stabilized semi-implicit schemes are used for temporal discretization, and the finite element method is used for spatial discretization. It is shown that by adding a single linear term that is of the same order with the truncation error in time, the proposed methods are all unconditionally energy stable. Error estimates for the two schemes are also established. Numerical examples are presented to confirm the accuracy, efficiency and stability of the proposed methods.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0046}, url = {http://global-sci.org/intro/article_detail/aamm/22933.html} }
TY - JOUR T1 - Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations AU - Li , Congying AU - Tang , Liang AU - Zhou , Jie JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 667 EP - 691 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0046 UR - https://global-sci.org/intro/article_detail/aamm/22933.html KW - Allen-Cahn equation, Cahn-Hilliard equation, stabilized semi-implicit method, energy stable, error estimation. AB -

In this paper, we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations. Stabilized semi-implicit schemes are used for temporal discretization, and the finite element method is used for spatial discretization. It is shown that by adding a single linear term that is of the same order with the truncation error in time, the proposed methods are all unconditionally energy stable. Error estimates for the two schemes are also established. Numerical examples are presented to confirm the accuracy, efficiency and stability of the proposed methods.

Congying Li, Liang Tang & Jie Zhou. (2024). Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations. Advances in Applied Mathematics and Mechanics. 16 (3). 667-691. doi:10.4208/aamm.OA-2023-0046
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