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)

96 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

Access to Document

10.1007/s11200-013-0141-2

Download pdf
© 2014 Inst. Geophys. AS CR, Prague
Accepted author manuscript, 494 KB

Cite this

@article{a82e620f8ced4e7d9977f11d709248a4,

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.",

keywords = "boundary elements, heat-kernel smoothing, Molodensky problem, Nash-H{\"o}rmander iteration",

author = "Lothar Banz and Adrian Costea and Heiko Gimperlein and Stephan, {Ernst P.}",

year = "2014",

month = oct,

doi = "10.1007/s11200-013-0141-2",

language = "English",

volume = "58",

pages = "489--504",

journal = "Studia Geophysica et Geodaetica",

issn = "0039-3169",

publisher = "Springer",

number = "4",

}

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.

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

SN - 0039-3169

VL - 58

SP - 489

EP - 504

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

Access to Document

Fingerprint

Cite this