Spline approximation of gradient fields: Applications to wind velocity fields

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• 作者：Carole Le Guyader ; Dominique Apprato ; Christian Gout
• 关键词：41A15 ; 41A25 ; 68U10
• 刊名：Mathematics and Computers in Simulation
• 出版年：March, 2014
• 年：2014
• 卷：97
• 期：Complete
• 页码：260-279
• 全文大小：7360 K

文摘

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 D^m-splines.