Construction of global surfaces by variational evolutionary PDE splines

Abstract: This paper deals with the construction and characterization of discrete variational PDE splines. To formulate the problem, we need an evolutionary PDE equation, certain boundary conditions and a set of points to approximate. We show the existence and the uniqueness of the solution of such a problem and we establish a convergence result of a discrete variational evolutionary PDE spline to a given function. We present several numerical and graphical examples of construction and approximation of surfaces in order to prove the validity of the presented method. [Copyright &y& Elsevier]