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2013 Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems
Pius W. M. Chin
J. Appl. Math. 2013: 1-9 (2013). DOI: 10.1155/2013/520219

Abstract

The optimal rate of convergence of the wave equation in both the energy and the L2-norms using continuous Galerkin method is well known. We exploit this technique and design a fully discrete scheme consisting of coupling the nonstandard finite difference method in the time and the continuous Galerkin method in the space variables. We show that, for sufficiently smooth solution, the maximal error in the L2-norm possesses the optimal rate of convergence O(h2+(Δt)2) where h is the mesh size and Δt is the time step size. Furthermore, we show that this scheme replicates the properties of the exact solution of the wave equation. Some numerical experiments should be performed to support our theoretical analysis.

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Pius W. M. Chin. "Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/520219

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950725
MathSciNet: MR3147897
Digital Object Identifier: 10.1155/2013/520219

Rights: Copyright © 2013 Hindawi

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