1. Numerical approximation using evolution PDE variational splines
- Author
-
Zakaria Belhaj, A. Kouibia, and Miguel Pasadas
- Subjects
Splines ,Numerical Analysis ,Partial differential equation ,Box spline ,Applied Mathematics ,Finite elements ,Mathematical analysis ,010103 numerical & computational mathematics ,PDE ,01 natural sciences ,Finite element method ,Interpolation ,Surfaces ,010101 applied mathematics ,Computational Mathematics ,PDE surface ,Position (vector) ,Partial derivative ,Uniqueness ,Boundary value problem ,0101 mathematics ,Approximation ,Analysis ,Mathematics - Abstract
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
- Published
- 2017