چکیده (انگلیسی):

This work deals with an approximation method for multivariate functions from data constituted by a given data point set and a partial differential equation (PDE). The solution of our problem is called a PDE spline.We establish a variational characterization of the PDE spline and a convergence result of it to the function which the data are obtained.We estimate the order of the approximation error and finally, we present an example to illustrate the fitting method.