Wind velocity field approximation from sparse data

The problem of vector field approximation emerges in a wide range of fields such as: motion control, computer vision, geometrical analysis, geometrical design, analysis of acoustic and/or electromagnetic waves, as well as in geophysics, medical imaging, fluid mechanics and so on... 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, PDE-based methods, spline and Rational Basis Function approximations.. The originality of this work consists: - in considering that the vector field derives from a potential (conservative vector field): it occurs for instance in meteorology (winds derive from temperature potentials), oceanography (currents derive from pression potentials), image processing... For in land wind velocity field, we also take into account the topography effects. - of a rigorous study of existence-uniqueness of the solution of the problem phrased as an energy minimization, - in establishing a convergence result (while many approaches only give algorithms without mathematical study) and providing an approximation error estimate. - in using a specific visualization tool.