High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917964659294208 |
|---|---|
| author | Xiao, Jingjing Liu, Ying Yi, Nianyu |
| author_facet | Xiao, Jingjing Liu, Ying Yi, Nianyu |
| contents | This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection refinement has been well established, in practical computations, the use of non-asymptotic exact of error estimator and the excessive number of adaptive iteration steps often lead to inefficiency of the adaptive algorithm. We propose an efficient adaptive finite element method based on high-accuracy techniques including the superconvergence recovery technique and high-quality mesh optimization. The centroidal Voronoi Delaunay triangulation mesh optimization is embedded in the mesh adaption to provide high-quality mesh, and then assure that the superconvergence property of the recovered gradient and the asymptotical exactness of the error estimator. A tailored adaptive strategy, which could generate high-quality meshes with a target number of vertices, is developed to ensure the adaptive computation process terminated within $7$ steps. The effectiveness and robustness of the adaptive algorithm is numerically demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs Xiao, Jingjing Liu, Ying Yi, Nianyu Numerical Analysis This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection refinement has been well established, in practical computations, the use of non-asymptotic exact of error estimator and the excessive number of adaptive iteration steps often lead to inefficiency of the adaptive algorithm. We propose an efficient adaptive finite element method based on high-accuracy techniques including the superconvergence recovery technique and high-quality mesh optimization. The centroidal Voronoi Delaunay triangulation mesh optimization is embedded in the mesh adaption to provide high-quality mesh, and then assure that the superconvergence property of the recovered gradient and the asymptotical exactness of the error estimator. A tailored adaptive strategy, which could generate high-quality meshes with a target number of vertices, is developed to ensure the adaptive computation process terminated within $7$ steps. The effectiveness and robustness of the adaptive algorithm is numerically demonstrated. |
| title | High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2503.17234 |