Surface finite element approximation of parabolic SPDEs with Whittle--Matérn noise
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916999679967232 |
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| author | Auestad, Øyvind Stormark Fuglstad, Geir-Arne Lang, Annika |
| author_facet | Auestad, Øyvind Stormark Fuglstad, Geir-Arne Lang, Annika |
| contents | We propose and analyse a new type of fully discrete surface finite element approximation of a class of linear parabolic stochastic evolution equations with additive noise. Our discretization uses a surface finite element approximation of the noise, and is tailored for equations with noise having covariance operator defined by (negative powers of) elliptic operators, like Whittle--Matérn random fields. We derive strong and pathwise convergence rates of our approximation, and verify these by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surface finite element approximation of parabolic SPDEs with Whittle--Matérn noise Auestad, Øyvind Stormark Fuglstad, Geir-Arne Lang, Annika Numerical Analysis Probability 65C30, 65C20, 35K10, 35K51, 60H15 We propose and analyse a new type of fully discrete surface finite element approximation of a class of linear parabolic stochastic evolution equations with additive noise. Our discretization uses a surface finite element approximation of the noise, and is tailored for equations with noise having covariance operator defined by (negative powers of) elliptic operators, like Whittle--Matérn random fields. We derive strong and pathwise convergence rates of our approximation, and verify these by numerical experiments. |
| title | Surface finite element approximation of parabolic SPDEs with Whittle--Matérn noise |
| topic | Numerical Analysis Probability 65C30, 65C20, 35K10, 35K51, 60H15 |
| url | https://arxiv.org/abs/2510.08443 |