Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915437765197824 |
|---|---|
| author | Dell'Accio, Francesco Desiderio, Luca Guessab, Allal Nudo, Federico |
| author_facet | Dell'Accio, Francesco Desiderio, Luca Guessab, Allal Nudo, Federico |
| contents | In this paper, we propose weighted and unweighted enrichment strategies to enhance the accuracy of the linear lagrangian finite element for solving the Poisson problem with Dirichlet boundary conditions. We first recall key examples of admissible enrichment functions, specifically designed to overcome the limitations of the linear lagrangian finite element in capturing solution features such as sharp gradients and boundary-layer phenomena. We then introduce two novel three-parameter families of weighted enrichment functions and derive an explicit error bound in $L^2$-norm. Numerical experiments confirm the effectiveness of the proposed approach in improving approximation accuracy, demonstrating its potential for a wide range of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions Dell'Accio, Francesco Desiderio, Luca Guessab, Allal Nudo, Federico Numerical Analysis In this paper, we propose weighted and unweighted enrichment strategies to enhance the accuracy of the linear lagrangian finite element for solving the Poisson problem with Dirichlet boundary conditions. We first recall key examples of admissible enrichment functions, specifically designed to overcome the limitations of the linear lagrangian finite element in capturing solution features such as sharp gradients and boundary-layer phenomena. We then introduce two novel three-parameter families of weighted enrichment functions and derive an explicit error bound in $L^2$-norm. Numerical experiments confirm the effectiveness of the proposed approach in improving approximation accuracy, demonstrating its potential for a wide range of applications. |
| title | Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.07238 |