Superclosenes error estimates for the div least-squares finite element method on elliptic problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912376294473728 |
|---|---|
| author | Chen, Gang Yang, Fanyi Zhang, Zheyuan |
| author_facet | Chen, Gang Yang, Fanyi Zhang, Zheyuan |
| contents | In this paper we provide some error estimates for the div least-squares finite element method on elliptic problems. The main contribution is presenting a complete error analysis, which improves the current \emph{state-of-the-art} results. The error estimates for both the scalar and the flux variables are established by specially designed dual arguments with the help of two projections: elliptic projection and H(div) projection, which are crucial to supercloseness estimates. In most cases, $H^3$ regularity is omitted to get the optimal convergence rate for vector and scalar unknowns, and most of our results require a lower regularity for the vector variable than the scalar. Moreover, a series of supercloseness results are proved, which are \emph{never seen} in the previous work of least-squares finite element methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superclosenes error estimates for the div least-squares finite element method on elliptic problems Chen, Gang Yang, Fanyi Zhang, Zheyuan Numerical Analysis 65N15, 65N30 In this paper we provide some error estimates for the div least-squares finite element method on elliptic problems. The main contribution is presenting a complete error analysis, which improves the current \emph{state-of-the-art} results. The error estimates for both the scalar and the flux variables are established by specially designed dual arguments with the help of two projections: elliptic projection and H(div) projection, which are crucial to supercloseness estimates. In most cases, $H^3$ regularity is omitted to get the optimal convergence rate for vector and scalar unknowns, and most of our results require a lower regularity for the vector variable than the scalar. Moreover, a series of supercloseness results are proved, which are \emph{never seen} in the previous work of least-squares finite element methods. |
| title | Superclosenes error estimates for the div least-squares finite element method on elliptic problems |
| topic | Numerical Analysis 65N15, 65N30 |
| url | https://arxiv.org/abs/2404.04918 |