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

Original language | English |
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Pages (from-to) | 489-504 |

Journal | Studia Geophysica et Geodaetica |

Volume | 58 |

Issue number | 4 |

Early online date | 8 May 2014 |

DOIs | |

State | Published - Oct 2014 |

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### Keywords

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

### Cite this

*Studia Geophysica et Geodaetica*,

*58*(4), 489-504. DOI: 10.1007/s11200-013-0141-2

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*Studia Geophysica et Geodaetica*, vol 58, no. 4, pp. 489-504. DOI: 10.1007/s11200-013-0141-2

**Numerical simulations for the non-linear Molodensky problem.** / Banz, Lothar; Costea, Adrian; Gimperlein, Heiko; Stephan, Ernst P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical simulations for the non-linear Molodensky problem

AU - Banz,Lothar

AU - Costea,Adrian

AU - Gimperlein,Heiko

AU - Stephan,Ernst P.

PY - 2014/10

Y1 - 2014/10

N2 - 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. © 2014 Institute of Geophysics of the ASCR, v.v.i.

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

KW - boundary elements

KW - heat-kernel smoothing

KW - Molodensky problem

KW - Nash-Hörmander iteration

U2 - 10.1007/s11200-013-0141-2

DO - 10.1007/s11200-013-0141-2

M3 - Article

VL - 58

SP - 489

EP - 504

JO - Studia Geophysica et Geodaetica

T2 - Studia Geophysica et Geodaetica

JF - Studia Geophysica et Geodaetica

SN - 0039-3169

IS - 4

ER -