Volume 20, Issue 6
On the Hp Finite Element Method for the One Dimensional Singularly Perturbed Convection-Diffusion Problems

Zhi Min Zhang

DOI:

J. Comp. Math., 20 (2002), pp. 599-610

Published online: 2002-12

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  • 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.

  • Keywords

hp-version finite element methods convection-diffusion singularly perturbed exponential

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@Article{JCM-20-599, author = {}, title = {On the Hp Finite Element Method for the One Dimensional Singularly Perturbed Convection-Diffusion Problems}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8945.html} }
TY - JOUR T1 - On the Hp Finite Element Method for the One Dimensional Singularly Perturbed Convection-Diffusion Problems JO - Journal of Computational Mathematics VL - 6 SP - 599 EP - 610 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8945.html KW - hp-version finite element methods KW - convection-diffusion KW - singularly perturbed KW - exponential AB - 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.
Zhi Min Zhang. (1970). On the Hp Finite Element Method for the One Dimensional Singularly Perturbed Convection-Diffusion Problems. Journal of Computational Mathematics. 20 (6). 599-610. doi:
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