Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers

Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers

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.