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

This paper deals with the construction and characterization of discrete PDE splines on a polygonal domain. For this purpose, we need a PDE equation (usually an elliptic PDE), certain boundary conditions and a set of points to approximate. We thus demonstrate 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. To illustrate, we provide several numerical and graphic examples of construction and approximation by discrete PDE splines.