Volume 1, Issue 2
Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 138-149.

Published online: 2008-01

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• 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.

• Keywords

Finite element methods, singularly perturbed problems, uniformly convergent.

65M60, 65M12, 65M15

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@Article{NMTMA-1-138, author = {}, title = {Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6045.html} }
TY - JOUR T1 - Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 138 EP - 149 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6045.html KW - Finite element methods, singularly perturbed problems, uniformly convergent. AB -

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.

Jichun Li & Yitung Chen. (2020). Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers. Numerical Mathematics: Theory, Methods and Applications. 1 (2). 138-149. doi:
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