  The thin plate spline is a popular tool for the interpolation and smoothing
of scattered data. In this paper we propose a novel stabilized mixed finite
element method for the discretization of thin plate splines. The mixed
formulation is obtained by introducing the gradient of the smoother as an
additional unknown. Working with a pair of bases for the gradient of the
smoother and the Lagrange multiplier which forms a biorthogonal system, we can
easily eliminate these two variables (gradient of the smoother and Lagrange
multiplier) leading to a positive definite formulation. The optimal a priori
estimate is proved by using a superconvergence property of a gradient recovery
operator.
