Bathymetry reconstruction using inverse shallow water models: Finite element discretization and regularization
| dc.contributor.author | Hajduk, Hennes | |
| dc.contributor.author | Kuzmin, Dmitri | |
| dc.contributor.author | Aizinger, Vadym | |
| dc.date.accessioned | 2018-05-23T13:37:56Z | |
| dc.date.available | 2018-05-23T13:37:56Z | |
| dc.date.issued | 2018-04 | |
| dc.description.abstract | In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner. | en |
| dc.identifier.issn | 2190-1767 | |
| dc.identifier.uri | http://hdl.handle.net/2003/36876 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-18875 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Ergebnisberichte des Instituts für Angewandte Mathematik;585 | |
| dc.subject | Bathymetry reconstruction | en |
| dc.subject | shallow water equations | en |
| dc.subject | continuous/ discontinuous Galerkin method | en |
| dc.subject | inverse problem | en |
| dc.subject.ddc | 610 | |
| dc.subject.rswk | Bathymetrie | de |
| dc.subject.rswk | Galerkin-Methode | de |
| dc.title | Bathymetry reconstruction using inverse shallow water models: Finite element discretization and regularization | en |
| dc.type | Text | |
| dc.type.publicationtype | preprint | |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |