Finite Element Simulation for Fractional Allen–Cahn Equation with Regularized Logarithmic Free Energy Article Swipe
Feng Wang
,
Huanzhen Chen
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9080488
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9080488
This paper is focused on developing a Galerkin finite element framework for the fractional Allen–Cahn equation with regularized logarithmic potential over the Rd (d=1,2,3) domain, where the regularization of the singular potential extends beyond the classical double-well formulation. A fully discrete finite element scheme is developed using a k-th-order finite element space for spatial approximation and a backward Euler scheme for the temporal discretization of a regularized system. The existence and uniqueness of numerical solutions are rigorously established by applying Brouwer’s fixed-point theorem. Moreover, the proposed numerical framework is shown to preserve the discrete energy dissipation law analytically, while a priori error estimates are derived. Finally, numerical experiments are conducted to verify the theoretical results and the inherent physical property, such as phase separation phenomenon and coarsening processes. The results show that the fractional Allen–Cahn model provides enhanced capability in capturing phase transition characteristics compared to its classical equation.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/fractalfract9080488
- OA Status
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- References
- 32
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- 10
- OpenAlex ID
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https://doi.org/10.3390/fractalfract9080488Digital Object Identifier
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Finite Element Simulation for Fractional Allen–Cahn Equation with Regularized Logarithmic Free EnergyWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-07-24Full publication date if available
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Feng Wang, Huanzhen ChenList of authors in order
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https://doi.org/10.3390/fractalfract9080488Publisher landing page
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.3390/fractalfract9080488Direct OA link when available
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Allen–Cahn equation, Finite element method, Logarithm, Energy (signal processing), Mathematics, Physics, Mathematical analysis, Thermodynamics, StatisticsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.theoretical | 113 |
| abstract_inverted_index.Allen–Cahn | 14, 134 |
| abstract_inverted_index.formulation. | 37 |
| abstract_inverted_index.analytically, | 97 |
| abstract_inverted_index.approximation | 54 |
| abstract_inverted_index.discretization | 63 |
| abstract_inverted_index.regularization | 27 |
| abstract_inverted_index.characteristics | 143 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5101743303, https://openalex.org/A5101770324 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I28006308, https://openalex.org/I80143920 |
| citation_normalized_percentile.value | 0.27057579 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |