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[Text] / E. Dementyeva, E. Karepova, V. Shaidurov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (AMITANS '14). Ser. AIP Conference Proceedings. - 2014. - Vol. 1629: 6th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) (JUN 26-JUL 01, 2014, Albena, BULGARIA). - P373-380, DOI 10.1063/1.4902297. - Cited References: 18 . - ISSN 0094-243X. - ISSN 978-0-735РУБ Mathematics, Applied + Physics, Applied

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 problem 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.

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Держатели документа:
[Dementyeva, E.
Karepova, E.
Shaidurov, V.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН

Доп.точки доступа:
Dementyeva, E.V.; Дементьева, Екатерина Васильевна; Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaidurov, V.V.; Шайдуров, Владимир Викторович