Volume 1, Issue 2
The Convergence of Infinite Element Method for the Non-Similar Case

Lung-An Ying

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J. Comp. Math., 1 (1983), pp. 130-142

Published online: 1983-01

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  • Abstract

We have considered the infinite element method for a class of elliptic systems with constant coeffcients in [1]. this class can be characterized as : they have the invariance under similarity transformaations of independent variables. for example the laplace equation and the system of plane elastic equations have this property. we have suggested a technique to solve these problem by applying this property and a self similar discretization, and proved the convergence, not only the average convergence of the solutions has been discussed, but also term-by-term convergence for the expansions of the solutions, the second convergence manifests the advantage of the infinite element method, that is, the local singularity of the solutions can be calculated with high precision.

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@Article{JCM-1-130, author = {Lung-An Ying}, title = {The Convergence of Infinite Element Method for the Non-Similar Case}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {2}, pages = {130--142}, abstract = { We have considered the infinite element method for a class of elliptic systems with constant coeffcients in [1]. this class can be characterized as : they have the invariance under similarity transformaations of independent variables. for example the laplace equation and the system of plane elastic equations have this property. we have suggested a technique to solve these problem by applying this property and a self similar discretization, and proved the convergence, not only the average convergence of the solutions has been discussed, but also term-by-term convergence for the expansions of the solutions, the second convergence manifests the advantage of the infinite element method, that is, the local singularity of the solutions can be calculated with high precision. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9689.html} }
TY - JOUR T1 - The Convergence of Infinite Element Method for the Non-Similar Case AU - Lung-An Ying JO - Journal of Computational Mathematics VL - 2 SP - 130 EP - 142 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9689.html KW - AB - We have considered the infinite element method for a class of elliptic systems with constant coeffcients in [1]. this class can be characterized as : they have the invariance under similarity transformaations of independent variables. for example the laplace equation and the system of plane elastic equations have this property. we have suggested a technique to solve these problem by applying this property and a self similar discretization, and proved the convergence, not only the average convergence of the solutions has been discussed, but also term-by-term convergence for the expansions of the solutions, the second convergence manifests the advantage of the infinite element method, that is, the local singularity of the solutions can be calculated with high precision.
Lung-An Ying. (1970). The Convergence of Infinite Element Method for the Non-Similar Case. Journal of Computational Mathematics. 1 (2). 130-142. doi:
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