High-Order Interior Penalty Finite Element Methods for Fourth-Order Phase-Field Models in Fracture Analysis
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913791820693504 |
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| author | Tian, Tian Chunyu, Chen Huayi, Wei |
| author_facet | Tian, Tian Chunyu, Chen Huayi, Wei |
| contents | This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy compared to traditional second-order phase-field models, particularly when simulating complex crack paths. The IP-FEM provides an efficient framework for discretizing these models, effectively handling nonconforming trial functions and complex boundary conditions.
In this study, we leverage the FEALPy framework to implement a flexible computational tool that supports high-order IP-FEM discretizations. Our results show that as the polynomial order increases, the mesh dependence of the phase-field model decreases, offering improved accuracy and faster convergence. Additionally, we explore the trade-offs between computational cost and accuracy with varying polynomial orders and mesh sizes. The findings offer valuable insights for optimizing numerical simulations of brittle fracture in practical engineering applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Order Interior Penalty Finite Element Methods for Fourth-Order Phase-Field Models in Fracture Analysis Tian, Tian Chunyu, Chen Huayi, Wei Numerical Analysis Analysis of PDEs This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy compared to traditional second-order phase-field models, particularly when simulating complex crack paths. The IP-FEM provides an efficient framework for discretizing these models, effectively handling nonconforming trial functions and complex boundary conditions. In this study, we leverage the FEALPy framework to implement a flexible computational tool that supports high-order IP-FEM discretizations. Our results show that as the polynomial order increases, the mesh dependence of the phase-field model decreases, offering improved accuracy and faster convergence. Additionally, we explore the trade-offs between computational cost and accuracy with varying polynomial orders and mesh sizes. The findings offer valuable insights for optimizing numerical simulations of brittle fracture in practical engineering applications. |
| title | High-Order Interior Penalty Finite Element Methods for Fourth-Order Phase-Field Models in Fracture Analysis |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2504.09810 |