Convergence of the Dirichlet-Neumann method for semilinear elliptic equations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913553302159360 |
|---|---|
| author | Engström, Emil |
| author_facet | Engström, Emil |
| contents | The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are only convergence results for some specific cases in one spatial dimension. The aim of this manuscript is therefore to prove that the Dirichlet-Neumann method converges for a class of semilinear elliptic equations on Lipschitz continuous domains in two and three spatial dimensions. This is achieved by first proving a new result on the convergence of nonlinear iterations in Hilbert spaces and then applying this result to the Steklov-Poincaré formulation of the Dirichlet-Neumann method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of the Dirichlet-Neumann method for semilinear elliptic equations Engström, Emil Numerical Analysis 65N55 (Primary) 35J61, 47J25 (Secondary) The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are only convergence results for some specific cases in one spatial dimension. The aim of this manuscript is therefore to prove that the Dirichlet-Neumann method converges for a class of semilinear elliptic equations on Lipschitz continuous domains in two and three spatial dimensions. This is achieved by first proving a new result on the convergence of nonlinear iterations in Hilbert spaces and then applying this result to the Steklov-Poincaré formulation of the Dirichlet-Neumann method. |
| title | Convergence of the Dirichlet-Neumann method for semilinear elliptic equations |
| topic | Numerical Analysis 65N55 (Primary) 35J61, 47J25 (Secondary) |
| url | https://arxiv.org/abs/2410.14339 |