A Nash-Hörmander iteration and boundary elements for the Molodensky problem

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Standard

A Nash-Hörmander iteration and boundary elements for the Molodensky problem. / Costea, Adrian ; Gimperlein, Heiko; Stephan, Ernst P.

I: Numerische Mathematik, Bind 127, 2014, s. 1-34.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Costea, A, Gimperlein, H & Stephan, EP 2014, 'A Nash-Hörmander iteration and boundary elements for the Molodensky problem', Numerische Mathematik, bind 127, s. 1-34. https://doi.org/10.1007/s00211-013-0579-8

APA

Costea, A., Gimperlein, H., & Stephan, E. P. (2014). A Nash-Hörmander iteration and boundary elements for the Molodensky problem. Numerische Mathematik, 127, 1-34. https://doi.org/10.1007/s00211-013-0579-8

Vancouver

Costea A, Gimperlein H, Stephan EP. A Nash-Hörmander iteration and boundary elements for the Molodensky problem. Numerische Mathematik. 2014;127:1-34. https://doi.org/10.1007/s00211-013-0579-8

Author

Costea, Adrian ; Gimperlein, Heiko ; Stephan, Ernst P. / A Nash-Hörmander iteration and boundary elements for the Molodensky problem. I: Numerische Mathematik. 2014 ; Bind 127. s. 1-34.

Bibtex

@article{a8080db965e34d268ed5ec3d608565ad,
title = "A Nash-H{\"o}rmander iteration and boundary elements for the Molodensky problem",
abstract = "We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash–H{\"o}rmander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral.Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.",
author = "Adrian Costea and Heiko Gimperlein and Stephan, {Ernst P.}",
year = "2014",
doi = "10.1007/s00211-013-0579-8",
language = "English",
volume = "127",
pages = "1--34",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - A Nash-Hörmander iteration and boundary elements for the Molodensky problem

AU - Costea, Adrian

AU - Gimperlein, Heiko

AU - Stephan, Ernst P.

PY - 2014

Y1 - 2014

N2 - We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash–Hörmander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral.Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.

AB - We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash–Hörmander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral.Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.

U2 - 10.1007/s00211-013-0579-8

DO - 10.1007/s00211-013-0579-8

M3 - Journal article

VL - 127

SP - 1

EP - 34

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

ER -

ID: 137753762