Numerical simulations for the non-linear Molodensky problem

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)489-504
JournalStudia Geophysica et Geodaetica
Volume58
Issue number4
Early online date8 May 2014
DOIs
StatePublished - Oct 2014

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boundary element method
smoothing
geophysics
gravity
simulation

Keywords

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

Cite this

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

In: Studia Geophysica et Geodaetica, Vol. 58, No. 4, 10.2014, p. 489-504.

Research output: Contribution to journalArticle

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year = "2014",
month = "10",
doi = "10.1007/s11200-013-0141-2",
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journal = "Studia Geophysica et Geodaetica",
issn = "0039-3169",
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Numerical simulations for the non-linear Molodensky problem. / Banz, Lothar; Costea, Adrian; Gimperlein, Heiko; Stephan, Ernst P.

In: Studia Geophysica et Geodaetica, Vol. 58, No. 4, 10.2014, p. 489-504.

Research output: Contribution to journalArticle

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

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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.

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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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SP - 489

EP - 504

JO - Studia Geophysica et Geodaetica

T2 - Studia Geophysica et Geodaetica

JF - Studia Geophysica et Geodaetica

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