# The Numerical Solution of the Boundary Function Inverse Problem for the Tidal Models

• Evgeniya Karepova
• Ekaterina Dementyeva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

## Abstract

The problem of propagation of long waves in a domain of an arbitrary form with the sufficiently smooth boundary on a sphere is considered. The boundary consists of “solid” parts passing along the coastline and “open liquid” parts passing through the water area. In general case the influence of the ocean through an open boundary is unknown and must be found together with components of a velocity vector and free surface elevation. For this purpose we use observation data of free surface elevation given only on a part of an “open liquid” boundary. We solve our ill-posed inverse problem by an approach based on the optimal control methods and adjoint equations theory.

## Keywords

data assimilation problem finite elements method and high performance computation

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