Numerical simulations for the non-linear Molodensky problem |
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Authors: | Lothar Banz Adrian Costea Heiko Gimperlein Ernst P Stephan |
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Institution: | 1.Institut für Angewandte Mathematik,Leibniz Universit?t Hannover,Hannover,Germany;2.Department of Mathematical Sciences,University of Copenhagen,Copenhagen,Denmark |
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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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