Finite Element Analysis of a Local Exponentially Fitted Scheme for Time-Dependent Convection-Diffusion Problems
Year: 1999
Author: Xing-Ye Yue, Li-Shang Jiang, Tsi-Min Shih
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 3 : pp. 225–232
Abstract
In [16], Stynes and O'Riordan(91) introduced a local exponentially fitted finite element (FE) scheme for a singularly perturbed two-point boundary value problem without turning-point. An $ε$-uniform $h^{1/2}$-order accuracy was obtain for the $ε$-weighted energy norm. And this uniform order is known as an optimal one for global exponentially fitted FE schemes (see [6, 7, 12]).
In present paper, this scheme is used to a parabolic singularly perturbed problem. After some subtle analysis, a uniformly in $ε$ convergent order $h|{\rm ln} h|^{1/2}+ τ$ is achieved ($h$ is the space step and $τ$ is the time step), which sharpens the results in present literature. Furthermore, it implies that the accuracy order in [16] is actually $h|{\rm ln} h|^{1/2}$ rather than $h^{1/2}$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1999-JCM-9097
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 3 : pp. 225–232
Published online: 1999-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Singularly perturbed Exponentially fitted Uniformly in $ε$ convergence Petrov-Galerkin finite element method.