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

Authors:
M. Pasadas;M. L. Rodríguez
Affiliations:
Dep. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;Dep. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

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.