Coerciveness of the linear gravimetric boundary-value problem and a geometrical interpretation

Holota, Petr

doi:10.1007/s001900050131

Cited by 54 publications

(30 citation statements)

References 8 publications

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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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“…From the mathematical point of view, FGBVP represents an exterior oblique derivative BVP for the Laplace equation, cf. (Koch and Pope 1972;Bjerhammar and Svensson 1983;Holota 1997). In the last decades several researchers have been dealing with such kind of BVP, e.g.…”

Section: Introductionmentioning

confidence: 99%

An upwind-based scheme for solving the oblique derivative boundary-value problem related to physical geodesy

Macák

Čunderlík

Mikula

et al. 2015

Journal of Geodetic Science

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Abstract:The paper presents a novel original upwindbased approach for solving the oblique derivative boundary value problem by the finite volume method. In this approach, the oblique derivative boundary condition is interpreted as a stationary advection equation for the unknown disturbing potential. Its approximation is then performed by using the first order upwind scheme taking into account information from inflow parts of the finite volume boundary only. When the numerical scheme is derived, numerical simulations in 2D and 3D domains are performed and the experimental order of convergence of the proposed algorithm is studied. Moreover a comparison with a solution by the central scheme previously used for this kind of problem is performed. Finally we present numerical experiments dealing with the global and local gravity field modelling.

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“…It has been shown in (s,n) and the use of components of the deflections of the vertical have been also discussed in Holota (1997. Eq.…”

Section: A(uv)= Jyfds (4)mentioning

confidence: 96%

“…(9) and (10) define the linearized gravimetric fixed boundary-value problem and we know that its solution T is the disturbing potential, cf. Holota (1997), which focuses on the weak theory of the problem. This theory was also discussed in Rozanov and Sanso (2003).…”

Section: A(uv)= Jyfds (4)mentioning

confidence: 99%

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Successive Approximations in the Solution of a Weakly Formulated Geodetic Boundary-Value Problem

Holota

International Association of Geodesy Symposia

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Abstract. For many purposes a sphere or an ellipsoid of revolution approximate the figure of the Earth fairly well. However, the Earth's topography causes effects that continuously stimulate a considerable research effort. In contrast to the concept of the so-called shrinking parameter in the classical treatment of the effect, successive approximations are applied within a weak formulation of the respective boundary-value problem in this paper. In this connection functional-analytic estimates are investigated so as to clarify the convergence of the iteration process. In particular the ellipticity of a bilinear form associated with the problem under consideration is discussed for the solution domain of an ellipsoidal boundary. The apparatus of ellipsoidal harmonics is substantially used for this purpose. Quantitative estimates for the respective parameters were derived, when the potential is assumed to follow a finite degree model.

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Coerciveness of the linear gravimetric boundary-value problem and a geometrical interpretation

Cited by 54 publications

References 8 publications

Spectral analysis of the subelliptic oblique derivative problem

Spectral analysis of the subelliptic oblique derivative problem

An upwind-based scheme for solving the oblique derivative boundary-value problem related to physical geodesy

Successive Approximations in the Solution of a Weakly Formulated Geodetic Boundary-Value Problem

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