曲边区域上定常Stokes方程的类Wilson元逼近

The Quasi-Wilson Element Method for the Stationary Stokes Equations in Domain with Curved Boundaries

本文讨论类Wilson元对曲边区域上定常Stokes方程的有限元逼近,在不需要试探函数u满足divu=0的条件下,克服了由区域变动、边界条件转换、曲边边界逼近以及类Wilson元非协调性等带来的困难,得到了H1-模的最优误差估计。所得结果在弥补以往文献不足的同时,进一步拓宽了类Wilson元的应用范围。

The quasi-Wilson nonconforming arbitrary quadrilateral element approximation to the stationary Stokes equations in the domain with curved boundaries is considered for the case of the trial function u not satisfying the condition divu=0. The difficulties arising from the domain changing, the boundary datum transferring, the curved boundaries approximating and the nonconformity of quasiWilson element are overcome, the optimal error estimate in H^1-norm is derived. Thus the deficiencies of existing studies are remedied, and the application of quasi-Wilson element is extended.