Numerical simulations for the non-linear Molodensky problem

Lothar Banz; Adrian Costea; Heiko Gimperlein; Ernst P. Stephan

doi:10.1007/s11200-013-0141-2

Numerical simulations for the non-linear Molodensky problem

Lothar Banz
, Adrian Costea
, Heiko Gimperlein
, Ernst P. Stephan

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

138 Downloads (Pure)

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.

Original language	English
Pages (from-to)	489-504
Journal	Studia Geophysica et Geodaetica
Volume	58
Issue number	4
Early online date	8 May 2014
DOIs	https://doi.org/10.1007/s11200-013-0141-2
Publication status	Published - Oct 2014

Keywords

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

ASJC Scopus subject areas

Geophysics
Geochemistry and Petrology

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10.1007/s11200-013-0141-2

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© 2014 Inst. Geophys. AS CR, Prague
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Cite this

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title = "Numerical simulations for the non-linear Molodensky problem",

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-H{\"o}rmander 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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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.

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.

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

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VL - 58

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JO - Studia Geophysica et Geodaetica

JF - Studia Geophysica et Geodaetica

IS - 4

ER -

Numerical simulations for the non-linear Molodensky problem

Abstract

Keywords

ASJC Scopus subject areas

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