Studia Geophysica et Geodaetica

, Volume 58, Issue 4, pp 489–504 | Cite as

Numerical simulations for the non-linear Molodensky problem

  • Lothar Banz
  • Adrian Costea
  • Heiko Gimperlein
  • Ernst P. Stephan
Article

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.

Keywords

Molodensky problem heat-kernel smoothing boundary elements Nash-Hörmander iteration 

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Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2014

Authors and Affiliations

  • Lothar Banz
    • 1
  • Adrian Costea
    • 1
  • Heiko Gimperlein
    • 2
  • Ernst P. Stephan
    • 1
  1. 1.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

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