TY - JOUR
T1 - Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation
JO - Journal of Computational Mathematics
VL - 2
SP - 227
EP - 242
PY - 2011
DA - 2011/04
SN - 29
DO - http://doi.org/10.4208/jcm.1009-m3113
UR - https://global-sci.org/intro/article_detail/jcm/8475.html
KW - Convergence, Singular perturbation, Convection-diffusion equation, Finite element method.
AB - <p style="text-align: justify;">In this paper, we establish a convergence theory for a finite element method with weighted basis functions for solving singularly perturbed convection-diffusion equations. The stability of this finite element method is proved and an upper bound $\mathcal{O}(h|\ln \varepsilon |^{3/2})$ for errors in the approximate solutions in the energy norm is obtained on the triangular Bakhvalov-type mesh. Numerical results are presented to verify the stability and the convergent rate of this finite element method.</p>