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Simulation of VLBI Observations to Determine a Global TRF for GGOS Read chapter Read first chapter

2018 | OriginalPaper | Chapter

On the Convergence of the h-p Finite Element Method for Solving Boundary Value Problems in Physical Geodesy

Authors : David Mráz, Milan Bořík, Jaroslav Novotný

Published in: International Symposium on Earth and Environmental Sciences for Future Generations

Publisher: Springer International Publishing

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Abstract

A geopotential model of the Earth is usually calculated using the Stokes coefficients. As computational power has increased, research is focusing more on new ways of gravity field modelling. The objective of this work is to study an application of the h-p finite element method for solving boundary value problems in physical geodesy. For the purpose of studying this method, we have formulated model boundary value problems with different boundary conditions. The algorithm for solving these test problems was designed and was subsequently implemented by the program. We derived a weak formulation for each model boundary value problem and also the corresponding finite element discretization. We used isoparametric reference elements with linear and quadratic shape functions. The authors present the application of the h and p methodologies for increasing the rate of convergence of our solution, discuss mesh generation for large domains, and also solve the model boundary value problem, which is similar to the geodetic boundary value problem.

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previous chapter The Linearized Fixed Gravimetric Boundary Value Problem and Its Solution in Spheroidal Approximation
next chapter Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem
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Metadata
Title
On the Convergence of the h-p Finite Element Method for Solving Boundary Value Problems in Physical Geodesy
Authors
David Mráz
Milan Bořík
Jaroslav Novotný
Copyright Year
2018
Publisher
Springer International Publishing
Book
International Symposium on Earth and Environmental Sciences for Future Generations

Print ISBN: 978-3-319-69169-5

Electronic ISBN: 978-3-319-69170-1

Copyright Year: 2018

DOI
https://doi.org/10.1007/1345_2016_237