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Abstract We present a smoothing method of a set of points to be approximated from a given boundary value problem for the modified Helmholtz equation. A solution of such problem will be called MH-spline. Two convergence results are carefully established. Some numerical and graphic examples are shown in order to test the validity of the method. [ABSTRACT FROM AUTHOR]

This article deals with a numerical approximation method using an evolutionary partial differential equation (PDE) by discrete variational splines in a finite element space. To formulate the problem, we need an evolutionary PDE equation with respect to the time and the position, certain boundary conditions and a set of approximating points. We show the existence and uniqueness of the solution and we study a computational method to compute such a solution. Moreover, we established a convergence result with respect to the time and the position. We provided several numerical and graphic examples of approximation in order to show the validity and effectiveness of the presented method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 34: 5-18, 2018 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the continuity of surfaces by a shape-blending process. Furthermore, we study the continuity of the ruled surfaces constructed by linear interpolation between two pairs of continuous curves. We give some conditions for the continuity of composite surfaces in a shape-blending process. A practical approach is proposed to maintain the continuity of Bézier surfaces pairs in a shape-blending process by adjusting the control points along the common boundary of the resulting surface-pair. We finish by proving and justifying the efficiency of the approaching method with some graphical examples. [Copyright &y& Elsevier]

Abstract: An approximation problem of parametric curves and surfaces is studied by a new kind of spline functions from some Lagrange or Hermite data set. We present an interpolation problem by minimizing a functional on a parametric finite element space in order to obtain the new notion of a spline. We call it discrete interpolating variational spline. We show how to compute in practice such spline and we carefully prove a convergence result. To illustrate the generality and practice of this work we give some particular cases and we finish by presenting some numerical and graphical examples. [Copyright &y& Elsevier]

Abstract: In this paper, we present an interpolation method for curves from a data set by means of the optimization of the parameters of a quadratic functional in a space of parametric cubic spline functions. The existence and the uniqueness of this problem are shown. Moreover, a convergence result of the method is established in order to justify the method presented. The aforementioned functional involves some real non-negative parameters; the optimal parametric curve is obtained by the suitable optimization of these parameters. Finally, we analyze some numerical and graphical examples in order to show the efficiency of our method. [Copyright &y& Elsevier]

Abstract: In this paper we present an approximation problem of parametric curves and surfaces from a Lagrange or Hermite data set. In particular, we study an interpolation problem by minimizing some functional on a Sobolev space that produces the new notion of interpolating variational spline. We carefully establish a convergence result. Some specific cases illustrate the generality of this work. [Copyright &y& Elsevier]

This paper deals with a shape preserving method of interpolating positive data at points of the plane in R2. 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 R2, 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. [Copyright &y& Elsevier]