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Finite element method for solving geodetic boundary value problems / Z. Faskova in Journal of geodesy, vol 84 n° 2 (February 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 2 (February 2010) . - pp 135 - 144 Titre : Finite element method for solving geodetic boundary value problems Type de document : Article/Communication Auteurs : Z. Faskova, Auteur ; Robert Cunderlik, Auteur ; Karol Mikula, Auteur Année de publication : 2010 Article en page(s) : pp 135 - 144 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] Earth Gravity Model 2008 [Termes IGN] géoïde [Termes IGN] méthode des éléments finis [Termes IGN] problème de Dirichlet [Termes IGN] problème des valeurs limites Résumé : (Auteur) The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions. Copyright Springer Numéro de notice : A2010-108 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0349-7 Date de publication en ligne : 13/10/2009 En ligne : https://doi.org/10.1007/s00190-009-0349-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30304 [article]

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