full
search.png

Search

close.png

Cancel

arrow
Volume 43, Issue 3
Numerical Energy Dissipation for Time-Fractional Phase-Field Equations

Chaoyu Quan, Tao Tang & Jiang Yang

DOI: 10.4208/jcm.2311-m2021-0199

J. Comp. Math., 43 (2025), pp. 515-539.

Published online: 2024-11

Preview Purchase PDF 13 135

Cited by

google scholar semantic scholar
Export citation
  • Abstract

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the corresponding theory for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy law. The extension for a $(2−α)$-order L1 scalar auxiliary variable scheme will be investigated. Moreover, we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time steps. Several numerical experiments are carried to verify our theoretical analysis.

  • Keywords

Time-fractional phased-field equation, Allen-Cahn equations, Cahn-Hilliard equations, Caputo fractional derivative, Energy dissipation.

  • AMS Subject Headings

65M06, 65M12, 74A50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-43-515, author = {Quan , ChaoyuTang , Tao and Yang , Jiang}, title = {Numerical Energy Dissipation for Time-Fractional Phase-Field Equations}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {3}, pages = {515--539}, abstract = {

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the corresponding theory for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy law. The extension for a $(2−α)$-order L1 scalar auxiliary variable scheme will be investigated. Moreover, we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time steps. Several numerical experiments are carried to verify our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2311-m2021-0199}, url = {http://global-sci.org/intro/article_detail/jcm/23548.html} }
TY - JOUR T1 - Numerical Energy Dissipation for Time-Fractional Phase-Field Equations AU - Quan , Chaoyu AU - Tang , Tao AU - Yang , Jiang JO - Journal of Computational Mathematics VL - 3 SP - 515 EP - 539 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2311-m2021-0199 UR - https://global-sci.org/intro/article_detail/jcm/23548.html KW - Time-fractional phased-field equation, Allen-Cahn equations, Cahn-Hilliard equations, Caputo fractional derivative, Energy dissipation. AB -

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the corresponding theory for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy law. The extension for a $(2−α)$-order L1 scalar auxiliary variable scheme will be investigated. Moreover, we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time steps. Several numerical experiments are carried to verify our theoretical analysis.

Quan , ChaoyuTang , Tao and Yang , Jiang. (2024). Numerical Energy Dissipation for Time-Fractional Phase-Field Equations. Journal of Computational Mathematics. 43 (3). 515-539. doi:10.4208/jcm.2311-m2021-0199
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard