Volume 1, Issue 2
The Error Bound of the Finite Element Method for a Two-Dimensional Singular Boundary Value Problem

Shu-Zi Zhou

DOI:

J. Comp. Math., 1 (1983), pp. 143-147

Published online: 1983-01

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  • Abstract

The finite element method for one-dimensioanl singular boundary valune problems have been studied by several authors. The finite element method for a two-dimensional singular boundary value problem is proposed in [12] recently [9]... and [3] have given the relevant theoretical studies. In[9], the error of order $O(h^k)$ has been proved for the lagrange elements of degree k provided that the solution of the boundary value problem is in $C^{k+1}(\Omega)$. [16] has proved the convergence of the linear finite element belongs to a weighted Sobolev space. For problem (1.1) in the present paper,[1] has proved that the error is of order O(h) for a variant linear element including a logarithmic term. for the ordinary linear element[15] and [3] have also obtained the error of order $O(h)$. In this paper we extend the result of [15] and [3] to elements of high degree.

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@Article{JCM-1-143, author = {Shu-Zi Zhou}, title = {The Error Bound of the Finite Element Method for a Two-Dimensional Singular Boundary Value Problem}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {2}, pages = {143--147}, abstract = { The finite element method for one-dimensioanl singular boundary valune problems have been studied by several authors. The finite element method for a two-dimensional singular boundary value problem is proposed in [12] recently [9]... and [3] have given the relevant theoretical studies. In[9], the error of order $O(h^k)$ has been proved for the lagrange elements of degree k provided that the solution of the boundary value problem is in $C^{k+1}(\Omega)$. [16] has proved the convergence of the linear finite element belongs to a weighted Sobolev space. For problem (1.1) in the present paper,[1] has proved that the error is of order O(h) for a variant linear element including a logarithmic term. for the ordinary linear element[15] and [3] have also obtained the error of order $O(h)$. In this paper we extend the result of [15] and [3] to elements of high degree. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9690.html} }
TY - JOUR T1 - The Error Bound of the Finite Element Method for a Two-Dimensional Singular Boundary Value Problem AU - Shu-Zi Zhou JO - Journal of Computational Mathematics VL - 2 SP - 143 EP - 147 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9690.html KW - AB - The finite element method for one-dimensioanl singular boundary valune problems have been studied by several authors. The finite element method for a two-dimensional singular boundary value problem is proposed in [12] recently [9]... and [3] have given the relevant theoretical studies. In[9], the error of order $O(h^k)$ has been proved for the lagrange elements of degree k provided that the solution of the boundary value problem is in $C^{k+1}(\Omega)$. [16] has proved the convergence of the linear finite element belongs to a weighted Sobolev space. For problem (1.1) in the present paper,[1] has proved that the error is of order O(h) for a variant linear element including a logarithmic term. for the ordinary linear element[15] and [3] have also obtained the error of order $O(h)$. In this paper we extend the result of [15] and [3] to elements of high degree.
Shu-Zi Zhou. (1970). The Error Bound of the Finite Element Method for a Two-Dimensional Singular Boundary Value Problem. Journal of Computational Mathematics. 1 (2). 143-147. doi:
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