Convergence analysis of a streamline diffusion method for a singularly perturbed convection-diffusion problem

Authors:
Zhongdi Cen;Lifeng Xi
Affiliations:
Zhejiang Wanli University, Institute of Mathematics, Ningbo, P. R. China;Zhejiang Wanli University, Institute of Mathematics, Ningbo, P. R. China
Venue:
WSEAS Transactions on Mathematics
Year:
2008

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Abstract

A streamline diffusion finite element method (SDFEM) is applied to a singularly perturbed convection-diffusion two-point boundary value problem in conservative form. The stability and accuracy of the SDFEM on arbitrary grids are studied. We derive the pointwise error estimates and the approximation of derivatives. These bounds are then made explicit for the particular cases of Shishkin-type meshes. Numerical experiments support our theoretical results.