Stability and Convergence of HDG Schemes under Minimal Regularity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912798519328768 |
|---|---|
| author | Jiang, Jiannan Walkington, Noel J. Yue, Yukun |
| author_facet | Jiang, Jiannan Walkington, Noel J. Yue, Yukun |
| contents | Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme converge at optimal rates to smooth solutions, this does not establish the stability of the method or convergence to solutions with minimal regularity. The compactness and convergence results show that the HDG scheme can be utilized for the solution of nonlinear problems and linear problems with non-smooth coefficients on domains with reentrant corners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability and Convergence of HDG Schemes under Minimal Regularity Jiang, Jiannan Walkington, Noel J. Yue, Yukun Numerical Analysis 65N12, 65N30 Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme converge at optimal rates to smooth solutions, this does not establish the stability of the method or convergence to solutions with minimal regularity. The compactness and convergence results show that the HDG scheme can be utilized for the solution of nonlinear problems and linear problems with non-smooth coefficients on domains with reentrant corners. |
| title | Stability and Convergence of HDG Schemes under Minimal Regularity |
| topic | Numerical Analysis 65N12, 65N30 |
| url | https://arxiv.org/abs/2310.18448 |