On the $hp$ Finite Element Method for the One Dimensional Singularly Perturbed Convection-Diffusion Problems
Year: 2002
Author: Zhi-Min Zhang
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 599–610
Abstract
In this work, a singularly perturbed two-point boundary value problem of convection-diffusion type is considered. An $hp$ version finite element method on a strongly graded piecewise uniform mesh of Shishkin type is used to solve the model problem. With the analytic assumption of the input data, it is shown that the method converges exponentially and the convergence is uniformly valid with respect to the singular perturbation parameter.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JCM-8945
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 599–610
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: $hp$-version finite element methods convection-diffusion singularly perturbed exponential rate of convergence.