凹角域上Green函数有限元逼近的逐点估计及有限元外推

本文运用权范数方法证明了多角形区域上Green函数有限元逼近的逐点估计 |G_z(x)-G_z~h(x)|≤C(h~|lnh|~3/|x-z|~α),?x,z∈Ω,其中C为与x,z,h无关的常数θ<α<β_M,β_M=π/α_M,α_M为Ω的最大内角.由此可导出凹角域上有限元逼近的渐近展开. 考虑模型问题

ERROR ESTIMATES FOR FINIT ELEMENT GREEN FUNCTION ON CONCAVE POLYGON

Using weighted norms we obtain in this paper some estimates of the error of discrete Greenfunction for elliptic boundary value problems on concave polysonal domain. From these re-sults we derive the asympsotic expansion for finite element approximation on convace do-main.