Mesh refinement and windowing near edges for some elliptic problem
Mesh refinement and windowing near edges for some elliptic problem
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DOI：
10.1137/0731037
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发表时间：
1994-06
影响因子：
2.9
通讯作者：
T. Apel;B. Heinrich
中科院分区：
文献类型：
--
作者：
T. Apel;B. Heinrich
三维边域椭圆问题的解一般都含有奇异性，这影响了标准有限元法的收敛阶。本文针对一类具有特殊而典型的边奇异函数的椭圆型问题，研究了适当的局部网格加密方法。证明了关于${\text{L}}_2 $-和${\text{W}}^{1，2} $-范数的收敛速度的估计，并且导出了与这种逼近相关的矩阵的条件数的界.通过对子域的误差估计，证明了两步有限元离散（加窗技术）的合理性。
The solutions of elliptic problems in three-dimensional domains with edges contain singularities, in general, which influence the order of convergence of the standard finite element method. In this paper, for some elliptic problem with a special, but typical edge singularity function, an appropriate local mesh refinement is studied. Estimates of the rate of convergence with respect to the ${\text{L}}_2 $- and ${\text{W}}^{1,2} $-norm are proved and, moreover, bounds of the condition number of the matrix associated with this approximation are derived. By means of some error estimates for subdomains, the justification of a two-step finite element discretization (windowing-technique) is given.