Numerical solution of the linearized fixed gravimetric boundary-value problem

Čunderlík, Róbert; Mikula, Karol; Mojzes, M.

doi:10.1007/s00190-007-0154-0

Cited by 50 publications

(12 citation statements)

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“…(II) In the near future, we would like to apply Theorems 2.3 and 10.1 to provide numerical solutions of the linearized fixed gravimetric boundary value problem on the real Earth surface topography in the degenerate (non-coercive) case, generalizing Holota [12] and Čunderlík-Mikula-Mojzeš [7].…”

Section: Proof Of Theorem 23 Via Boutet De Monvel Calculusmentioning

confidence: 99%

Spectral analysis of the subelliptic oblique derivative problem

Taira

2017

Arkiv För Matematik

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Abstract.This paper is devoted to a functional analytic approach to the subelliptic oblique derivative problem for the usual Laplacian with a complex parameter λ. We solve the long-standing open problem of the asymptotic eigenvalue distribution for the homogeneous oblique derivative problem when |λ| tends to ∞. We prove the spectral properties of the closed realization of the Laplacian similar to the elliptic (non-degenerate) case. In the proof we make use of Boutet de Monvel calculus in order to study the resolvents and their adjoints in the framework of L 2 Sobolev spaces.

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Section: Proof Of Theorem 23 Via Boutet De Monvel Calculusmentioning

confidence: 99%

Spectral analysis of the subelliptic oblique derivative problem

Taira

2017

Arkiv För Matematik

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“…De fato, esse também é um problema não-linear. Após a linearização (ČUNDERLÍK et al, 2008), o resultado é um PVCG gravimétrico fixo de derivada oblíqua, sendo a direção da derivada na superfície de contorno idêntica com a direção normal do vetor de gravidade normal gradU = γ (HECK,1989b).…”

Section: O Pvcg "Gravimétrico Fixo"unclassified

Problema de valor de contorno da Geodésia: uma abordagem conceitual

Guimarães

Blitzkow

2011

Bol. Ciênc. Geod.

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RESUMOUm dos problemas da Geodésia é determinar o campo de gravidade externo às massas, além da superfície limitante, bem como a variação temporal do mesmo. Stokes propôs no século XVIII uma formulação para a solução desse problema, porém implicava em algumas dificuldades. A formulação proposta por Molodensky em meados do século XX abriu uma nova perspectiva para a solução do problema. Ao longo dos anos, na Geodésia, a relevância do Problema de Valor de Contorno da Geodésia (PVCG) tem sido reconhecida como base teórica para essa disciplina. Além disso, o PVCG ganhou novo impulso com a era espacial e com o passar dos anos algumas alternativas foram elaboradas (super determinado, misto, solução de Brovar). Este trabalho tem como objetivo retratar as formulações de Stokes e Molodensky, bem como as principais alternativas do PVCG. Palavras-chave: Geodésia; Problema de Valor de Contorno; Superfície limitante. ABSTRACTOne of the Geodesy's problems is to determine the masses external gravity field, beyond the boundary surface, as well as the temporal variation. Stokes proposed a formulation in the 18 th century to solve this problem, however some problems were implied. The formulation proposed by Molodensky in the middle of the -20 th century opened a new perspective to solve this problem. Throughout the years, in Geodesy, the relevance of the Boundary Value Problem of Geodesy (BVPG) has been recognized as a theoretical basis for that discipline. In addition, the BVPG gained new impulse with the spatial era and in the maentime, many alternatives

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“…Concluding this summary it should be mentioned that instead of the analytical solutions also numerical solution procedures on the basis of boundary element methods (Klees, 1992(Klees, , 1998Lehmann, 1997;Lehmann and Klees, 1996;Klees et al, 2001;Čunderlík et al, 2008) or variational methods (Holota, 1997;Nesvadba et al, 2007) may be applied.…”

Section: Introductionmentioning

confidence: 98%

A Brovar-type solution of the fixed geodetic boundary-value problem

Heck

2011

Stud Geophys Geod

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For more than 150 years gravity anomalies have been used for the determination of geoidal heights, height anomalies and the external gravity field. Due to the fact that precise ellipsoidal heights could not be observed directly, traditionally a free geodetic boundary-value problem (GBVP) had to be formulated which after linearisation is related to gravity anomalies. Since nowadays the three-dimensional positions of gravity points can be determined by global navigation satellite systems very precisely, the modern formulation of the GBVP can be based on gravity disturbances which are related to a fixed GBVP using the known topographical surface of the Earth as boundary surface. The paper discusses various approaches into the solution of the fixed GBVP which after linearization corresponds to an oblique-derivative boundary-value problem for the Laplace equation. Among the analytical solution approaches a Brovar-type solution is worked out in detail, showing many similarities with respect to the classical solution of the scalar free GBVP.

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Numerical solution of the linearized fixed gravimetric boundary-value problem

Cited by 50 publications

References 20 publications

Spectral analysis of the subelliptic oblique derivative problem

Spectral analysis of the subelliptic oblique derivative problem

Problema de valor de contorno da Geodésia: uma abordagem conceitual

A Brovar-type solution of the fixed geodetic boundary-value problem

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