曲边区域非齐次Dirichlet问题的类Wilson元逼近

SOLVING NONHOMOGENOUS DIRICHLET BOUNDARY PROBLEMS IN DOMAINS WITH CURVED BOUNDARIES BY LIKE WILSON ELEMENT METHOD

1.引言 本文考虑用类Wilson元求解曲边区域Ω上的非齐次Dirichlet问题.对于曲边区域上的Dirichlet问题,常见的方法是将剖分加密,使近似求解区域Ωh尽可能地逼近Ω.并得到Ωh上的收敛性,如Ciarlet[4]等.但很多时候,Ω\Ωh上的误差估计是必要的.文[1]等对于齐次Dirichlet问题,考虑了Ω\Ωh上的影响.文[2]利用线性协调元考虑了非齐次Dirichlet问题的解u和有限元解uh在Ω\Ωh上的误差.

In this paper, we solve nonhomegeneous Dirichlet problems in domains with curved boundaries by arbitary quadrilateral like Wilson-element method. The approximate domains Ωh are polygonal. We transfer the boundary datum on (?)Ω to those on (?)Ωh by projection. We use some skills to do with the difficulties coming with the changed domain and boundary datum and the nonconforming element. The optimal-error estimates with energy norm and L2-norm are obtained both in Ωh and Ω \Ωh.