Abstract.
Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e 2 0)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant.
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Received: 5 June 1997 / Accepted: 20 February 1998
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Martinec, Z. Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition. Journal of Geodesy 72, 460–472 (1998). https://doi.org/10.1007/s001900050185
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DOI: https://doi.org/10.1007/s001900050185