A mixed finite element discretisation of thin-plate splines

Thin-plate splines are a well established technique for the inter- polation and smoothing of scattered data. However, the traditional formulation of the method leads to large, dense and often ill-conditioned matrices, which reduces its applicability in practice. We present a new mixed finite element formulation based on the ideas behind the mortar finite element methods. The resulting system of equations is sparse and positive de finite, and its size depends only on the number of finite elements not the number of data points.