The finite element approximation of vector fields in curvilinear coordinates

Dzhabrailov, A. Sh.; Klochkov, Yu. V.; Marchenko, S. S.; Николаев, А. П.

doi:10.3103/s1068799807020018

Cited by 6 publications

(2 citation statements)

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“…Many different approaches have been introduced to solve each specific problem occuring in the above fields of investigation. One can mention for instance: finite element approximation (see Dzhabrailov et al [14]), PDE-based methods (see Amodei and Benbourhim [1]), spline and Rational Basis Function approximations (see Awanou and Lai [6], Dodu and Rabut [11], Benbourhim and Bouhamidi [7]- [8], Ettl-Lowitsch et al [15,17,18], Zhou et al [25]...).…”

Section: Introductionmentioning

confidence: 99%

Spline approximation of gradient fields: Applications to wind velocity fields

Guyader¹,

Apprato²,

Gout³

2014

Mathematics and Computers in Simulation

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We study a spline-based approximation of vector fields in the conservative case. This problem appears for instance when approximating current or wind velocity fields, the data deriving in those cases from a potential (pressure for the wind, etc..). In the modelling, we introduce a minimization problem on an Hilbert space for which the existence and uniqueness of the solution are provided. A convergence result in the introduced Sobolev space is established using norm equivalence and compactness arguments, as well as an approximation error estimate of the involved smoothing D m-splines.

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Section: Introductionmentioning

confidence: 99%

Spline approximation of gradient fields: Applications to wind velocity fields

Guyader¹,

Apprato²,

Gout³

2014

Mathematics and Computers in Simulation

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“…The authors establish the existence and uniqueness of the solution, they also give convergence result in the introduced Sobolev space using norm equivalence and compactness arguments. Elsewhere, we can also mention several other approaches to study this problem: finite element approximation (see Dzhabrailov et al [9]), PDE-based methods (see Amodei and Benbourhim [1]), spline and RBF approximations (see Awanou and Lai [2], Dodu and Rabut [7], Benbourhim and Bouhamidi [3]- [4], Ettl-Lowitsch et al [10,23,24]).…”

Section: Introductionmentioning

confidence: 99%