The Finite Element Method as a Tool to Solve the Oblique Derivative Boundary Value Problem in Geodesy

Marek Macák; Zuzana Minarechová; Róbert Čunderlík; Karol Mikula

doi:10.2478/tmmp-2020-0005

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The Finite Element Method as a Tool to Solve the Oblique Derivative Boundary Value Problem in Geodesy

Tatra Mountains Mathematical Publications

Volume 75 (2020): Issue 1 (April 2020)

By: Marek Macák, Zuzana Minarechová, Róbert Čunderlík and Karol Mikula

Open Access

|Apr 2020

Abstract

In this paper, we propose a novel approach to approximate the solution of the Laplace equation with an oblique derivative boundary condition by the finite element method. We present and analyse diverse testing experiments to study its behaviour and convergence. Finally, the usefulness of this approach is demonstrated by using it to gravity field modelling, namely, to approximate the solution of a geodetic boundary value problem in Himalayas.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2020-0005 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 63 - 80

Submitted on: Apr 30, 2019

Published on: Apr 24, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

oblique derivative boundary value problem,

finite element method

Related subjects:

Mathematics,

General mathematics

© 2020 Marek Macák, Zuzana Minarechová, Róbert Čunderlík, Karol Mikula, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 75 (2020): Issue 1 (April 2020)