Year: 2008
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 138–149
Abstract
In this paper, using Lin's integral identity technique, we prove the optimal uniform convergence $O(N_x^{-2}\ln^2N_x+N_y^{-2}\ln^2N_y)$ in the $L^2$-norm for singularly perturbed problems with parabolic layers. The error estimate is achieved by bilinear finite elements on a Shishkin type mesh. Here $N_x$ and $N_y$ are the number of elements in the $x$- and $y$-directions, respectively. Numerical results are provided supporting our theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6045
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 138–149
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Finite element methods singularly perturbed problems uniformly convergent.