Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation

Autor:	Xijun Yu, Xiang-Gui Li, Guang-Nan Chen
Rok vydání:	2011
Předmět:	Computational Mathematics Spectral element method Mathematical analysis hp-FEM Basis function Mixed finite element method Convection–diffusion equation Upper and lower bounds Finite element method Extended finite element method Mathematics
Zdroj:	Journal of Computational Mathematics. 29:227-242
ISSN:	1991-7139 0254-9409
DOI:	10.4208/jcm.1009-m3113
Popis:	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 O(h|ln"| 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1e2876291e2daf0cf3ac30e363d1924f https://doi.org/10.4208/jcm.1009-m3113 Zobrazit plný text záznamu Plný text ve formátu PDF