Abstract
We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the Earth from the gravitational potential and the gravity vector. Our solution procedure solves a sequence of exterior oblique Robin problems and is based on a Nash-Hörmander iteration. We apply smoothing with the heat equation to overcome a loss of derivatives in the surface update. Numerical results show the error between the approximation and the exact solution in a model problem.
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Banz, L., Costea, A., Gimperlein, H. et al. Numerical simulations for the non-linear Molodensky problem. Stud Geophys Geod 58, 489–504 (2014). https://doi.org/10.1007/s11200-013-0141-2
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DOI: https://doi.org/10.1007/s11200-013-0141-2