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

Zhi-Min Zhang

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 rate of convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-599, author = {Zhang , Zhi-Min}, 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 AU - Zhang , Zhi-Min 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, convection-diffusion, singularly perturbed, exponential rate of convergence. 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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