A Nash-Hörmander iteration and boundary elements for the Molodensky problem
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We investigate the numerical approximation of the nonlinear Molodensky
problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash–Hörmander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m
steps, justify the use of smoothing operators based on the heat equation, and comment
on the accurate evaluation of the Hessian of the gravitational potential on the surface,
using a representation in terms of a hypersingular integral.Aboundary element method
is used to solve the exterior problem. Numerical results compare the error between
the approximation and the exact solution in a model problem.
Original language | English |
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Journal | Numerische Mathematik |
Volume | 127 |
Pages (from-to) | 1-34 |
ISSN | 0029-599X |
DOIs | |
Publication status | Published - 2014 |
ID: 137753762