<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Slovak University of Technology in Bratislava

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Apr 24, 2020

Page range: 63 - 80

Received: Apr 30, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0005

Keywords
oblique derivative boundary value problem, finite element method

© 2020 Marek Macák et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Apr 24, 2020

Page range: 63 - 80

Received: Apr 30, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0005

Keywordsoblique derivative boundary value problem, finite element method

© 2020 Marek Macák et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
oblique derivative boundary value problem, finite element method