Numerical Approximation using Evolution PDE Variational Splines
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Wiley Online Library
Kouibia Krichi, Abdelouahed; Pasadas Fernández, Miguel; Belhaj, Zakaria. Numerical Approximation using Evolution PDE Variational Splines. Numerical Methods for Partial Differential Equations, 34: 5–18, 2018 [http://hdl.handle.net/10481/50935]
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.