Shu-Zi Zhou ¹

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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