Variational bivariate interpolating splines with positivity constraints Original Research Article

This paper deals with a shape preserving method of interpolating positive data at points of the plane in View the MathML source. We formulate a problem in order to define a positive interpolation variational spline in the Sobolev space Hm(Ω), where Ω is a non-empty bounded set of View the MathML source, by minimizing the semi-norm of order m, and we discrete such problem in a finite element space. An algorithm allows us to compute the resulting function. Some convergence theorems are established. The error is of the order O(1/N)m when N tends to +∞, being N the number of the interpolating points. Some numerical and graphical examples are given in order to test the validity of this method.