有限元奇性问题的自适应处理

§1.引言 有限元奇性问题(包括凹角域问题以及方程本身的奇性等问题),由于奇点的存在,致使奇点附近收敛速度明显减慢。处理这一问题的有效方法是构作可靠实用的后验估计量来寻找收敛慢的坏单元,进行局部加密剖分,从而以最快的速度提高整体精度,但工作量最小。 本文的特点在于:1.对剖分条件限制较弱,只要求正规剖分(regular meshes)即

SELF-ADAPTIVE TREATMENT FOR FEM SINGULAR BOUNDARY VALUE PROBLEMS

Owing to the existence of singular points, the convergence rates of the appro-ximate solutions near singular points become apparently slow for FEM singular bo-undary value problems. In this paper, we provide and analyze an effective a-po-steriori estimator of the error in the FEM. These bounds are given explicitly fora certain concrete estimator for linear triangular elements and regular meshes. Anumerical example shows that the estimator of the error is very reasonable andconcise.