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Local modelling of sea surface topography from (geostrophic) ocean flow
Author(s) -
Fehlinger T.,
Freeden W.,
Gramsch S.,
Mayer C.,
Michel D.,
Schreiner M.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200710351
Subject(s) - boundary (topology) , differentiable function , geostrophic wind , mathematical analysis , simplicity , surface (topology) , flow (mathematics) , mathematics , domain (mathematical analysis) , boundary value problem , geometry , mechanics , physics , quantum mechanics
Calculating locally without boundary correction would lead to errors near the boundary. To avoid these Gibbs phenomenona we additionally consider the boundary integral of the corresponding region on the sphere which occurs in the integral formula of the solution. For reasons of simplicity we discuss a spherical cap first, that means we consider a continuously differentiable (regular) boundary curve. In a second step we concentrate on a more complicated domain with a non continuously differentiable boundary curve, namely a rectangular region. It will turn out that the boundary integral provides a major part for stabilizing and reconstructing the approximation of the solution in our multiscale procedure.