Smoothing and Filling Holes with Dirichlet Boundary Conditions

A commonly used method for the fitting of smooth functions to noisy data sets is the thin-plate spline method. Traditional thin-plate splines use radial basis functions and consequently requires the solution of a dense linear system of equations that grows with the number of data points. We present a method based instead on low order polynomial basis functions with local support defined on finite element grids. An advantage of such an approach is that the resulting system of equations is sparse and its size depends on the number of nodes in the finite element grid.