On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915071302565888 |
|---|---|
| author | Chen, Gang Han, Daozhi Singler, John Zhang, Yangwen |
| author_facet | Chen, Gang Han, Daozhi Singler, John Zhang, Yangwen |
| contents | We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully discrete scheme admits a unique solution, and we establish optimal convergence rates for all variables in the $L^2$ norm for arbitrary polynomial orders. In terms of the globally coupled degrees of freedom, the scalar variables are superconvergent. Another theoretical contribution of this work is a novel HDG Sobolev inequality that is useful for HDG error analysis of nonlinear problems. Numerical results are reported to confirm the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_00079 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation Chen, Gang Han, Daozhi Singler, John Zhang, Yangwen Numerical Analysis We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully discrete scheme admits a unique solution, and we establish optimal convergence rates for all variables in the $L^2$ norm for arbitrary polynomial orders. In terms of the globally coupled degrees of freedom, the scalar variables are superconvergent. Another theoretical contribution of this work is a novel HDG Sobolev inequality that is useful for HDG error analysis of nonlinear problems. Numerical results are reported to confirm the theoretical convergence rates. |
| title | On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1901.00079 |