Resumen de Bivariate approximation by discrete smoothing PDE splines

Miguel Luis Rodríguez González , Miguel Luis Rodríguez

• This paper deals with the construction and characterization of discrete PDE splines. For this purpose, we need a PDE equation (usually an elliptic PDE), certain boundary conditions and a set of points to approximate. We give two results about the convergence of a discrete PDE spline to a function of a fixed space in two different cases:

  (1) when the approximation points are fixed; (2) when the boundary points are fixed. We provide a numerical and graphic example of approximation by discrete PDE splines.