Adaptive strategies using standard and mixed finite elements for wind field adjustment

Abstract

In order to find a map of wind velocities, this study tries to obtain an incompressible wind field that adjusts to an experimental one: also verifying the corresponding boundary conditions of physical interest. This problem has been solved by several authors using finite differences or standard finite element techniques. In this paper, this problem is solved by two different adaptive finite element methods. The first makes use of standard finite element techniques, using linear interpolation of a potential function. In the second, a direct computation of the velocity field is undertaken by means of a mixed finite element method. Several error indicators are proposed for both formulations together with an adaptive strategy. We have applied both methods to several typical test problems, as well as to realistic data corresponding to the Island of Fuerteventura, with satisfactory results from a numerical point of view.