Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913647298609152 |
|---|---|
| author | Bullerjahn, Nils Kovács, Balázs |
| author_facet | Bullerjahn, Nils Kovács, Balázs |
| contents | A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions Bullerjahn, Nils Kovács, Balázs Numerical Analysis A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. |
| title | Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.20698 |