A nonconforming finite element method for data assimilation subject to the transient Stokes problem
In this study, we will consider the unique continuation problem for reconstructing the final state of the transient Stokes problem when the initial data is unknown, but additional data is given in a subdomain in space-time. The backward differentiation method is used to discretise the time derivativ...
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| Vydáno v: | Numerische Mathematik Ročník 157; číslo 6; s. 2017 - 2054 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Heidelberg
Springer Nature B.V
01.12.2025
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| Témata: | |
| ISSN: | 0029-599X, 0945-3245 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this study, we will consider the unique continuation problem for reconstructing the final state of the transient Stokes problem when the initial data is unknown, but additional data is given in a subdomain in space-time. The backward differentiation method is used to discretise the time derivative and standard nonconforming affine finite element approximation is applied for the discretisation in space. The discrete system is regularized by adding a penalty of the $$H^1$$ H 1 -semi-norm of the initial data, scaled with the mesh parameter. The scaling is chosen so that an optimal error estimate holds in $$L^2(T_1,T;H^1(\Omega ))$$ L 2 ( T 1 , T ; H 1 ( Ω ) ) , $$T_1>0$$ T 1 > 0 . The estimate is derived using the Lipschitz stability of the reconstruction problem and interpolation between discrete spaces. The theory is validated on some numerical examples. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0029-599X 0945-3245 |
| DOI: | 10.1007/s00211-025-01500-8 |