Error bounds for full space-time splitting discretizations of semi-linear SPDEs -- with a focus on dG domain decompositions
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_ | 1866915062937026560 |
|---|---|
| author | Eisenmann, Monika Hansen, Eskil Jans, Marvin |
| author_facet | Eisenmann, Monika Hansen, Eskil Jans, Marvin |
| contents | We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such methods can help to parallelize the code and therefore lead to a more efficient implementation. The domain decomposition is integrated through the Douglas-Rachford splitting scheme, where one split operator acts on one part of the domain. For an efficient space discretization of the underlying equation, we chose the discontinuous Galerkin method as this suits the parallelization strategy well. For this fully discretized scheme, we provide a strong space-time convergence result. We conclude the manuscript with numerical experiments validating our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error bounds for full space-time splitting discretizations of semi-linear SPDEs -- with a focus on dG domain decompositions Eisenmann, Monika Hansen, Eskil Jans, Marvin Numerical Analysis Probability 65C30, 60H35, 65M55, 60H15 We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such methods can help to parallelize the code and therefore lead to a more efficient implementation. The domain decomposition is integrated through the Douglas-Rachford splitting scheme, where one split operator acts on one part of the domain. For an efficient space discretization of the underlying equation, we chose the discontinuous Galerkin method as this suits the parallelization strategy well. For this fully discretized scheme, we provide a strong space-time convergence result. We conclude the manuscript with numerical experiments validating our theoretical findings. |
| title | Error bounds for full space-time splitting discretizations of semi-linear SPDEs -- with a focus on dG domain decompositions |
| topic | Numerical Analysis Probability 65C30, 60H35, 65M55, 60H15 |
| url | https://arxiv.org/abs/2412.10125 |