Recovery of a boundary function by observation data in a problem for the shallow water model


Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: 6th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2014; Flamingo Grand HotelAlbena, Bulgaria; Flamingo Grand HotelAlbena, Bulgaria

Год издания: 2014

Идентификатор DOI: 10.1063/1.4902297

Ключевые слова: Inverse problem, regularization methods, shallow water equations

Аннотация: In the paper, the shallow water equations are applied to describe the propagation of long waves in the coastal area of an ocean. The boundary condition involves an additional function on the open water boundary. In general case this function is unknown. For its determination an inverse problem is considered. To close the inverse prПоказать полностьюoblem the observation data on elevation of the sea surface along some part of the boundary is used. In actual, the observation data may have sufficiently large gaps. To improve the conditioning of this ill-posed inverse problem a regularization functional is considered that corresponds to higher smoothness of the data involved. The problem is solved numerically using optimal control methods, adjoint operators, and finite element method. As the result, the boundary function is recovered on the whole open water boundary including observations gaps. In the paper a solvability of the inverse problem is proved and the proposed numerical method is justified. The results are illustrated by a numerical example. © 2014 AIP Publishing LLC.

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Журнал: AIP Conference Proceedings

Выпуск журнала: Vol. 1629

Номера страниц: 373-380


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