Construction and approximation of surfaces by discrete PDE splines on a polygonal domain (Q960299)

The authors study the construction and characterization of discrete partial differential equations (PDE) smoothing spline surfaces on a polygonal domain. These are defined as solutions to a variational problem in a finite element space of functions satisfying certain boundary conditions. The minimized functional is made of two terms: the first least squares term measures the fitting error to scattered data in the interior of the domain, while the second (smoothing) term controls how well the surface is modelled by an elliptic PDE. The convergence of this smoothing method is studied and two numerical examples for the biharmonic operator on the unit square are presented.