Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 5 : pp. 488–508
Abstract
We analyze finite volume schemes of arbitrary order $r$ for the one-dimensional singularly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as $(N^{-1}ln(N+1))^r$, where $2N$ is the number of subintervals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order $(N^{-1}ln(N+1))^{2r}$, while at the Gauss points, the derivative error super-converges with order $(N^{-1}ln(N+1))^{r+1}$. All the above convergence and superconvergence properties are independent of the perturbation parameter $ε$. Numerical results are presented to support our theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1304-m4280
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 5 : pp. 488–508
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Finite Volume High Order Superconvergence Convection-Diffusion.