Spline approximation of gradient fields: applications to wind velocity fields

Carole Le Guyader (1) , Dominique Apprato (2) , Christian Gout (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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 modeling, 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 Dm-splines.

Domaines: Analyse numérique [math.NA]

Carole Le Guyader, Dominique Apprato, Christian Gout. Spline approximation of gradient fields: applications to wind velocity fields. Mathematics and Computers in Simulation, 2014, 97, pp.260--279. ⟨10.1016/j.matcom.2013.10.003⟩. ⟨hal-01022817⟩