三维Stokes问题Bernadi-Raugel元的超收敛

Superconvergence of the Bernadi-Raugel Mixed Finite Element Approximation for the Three-Dimensional Stokes Problem

考虑三维S tokes问题的一种混合有限元超收敛,采用满足B abuska-B rezz i条件的B ernad i-R auge l元,对三维空间中的立方体进行正则剖分,通过构造插值后处理算子以及应用B ram b le-H ibert引理得到的解精度提高一阶.

Superconvergence of a mixed finite element approximation for the three dimensional Stokes problem is presented. By using the Bernadi-Raugel mixed finite elements which satisfies the Babuska Brezzi condition a basic error is gained. Considering the problem on the piecewise uniform cuboid elements in the three-dimensional space, the convergence rate of the solution can be increased an order by using the interpolation and Bramble Hibert lemma.