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 - <p style="text-align: justify;">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.</p>