Approximation of vector fields using discrete div-rot variational splines in a finite element space

This paper deals with an approximation problem concerning vector fields through the new notion of div-rot variational splines. The minimizing problem is addressed in a finite element space through the choice of some semi-norms based on decomposition of the divergence operator and vector fields into a form with a rotational part. We study the existence and the uniqueness of the solution of such a problem. Then, a convergence result and an estimation of the error are established. Some numerical and graphical examples are analyzed in order to prove the validity of our method. Furthermore, we compare and show how our method improves upon one existing in the literature.