一种非协调有限元方法的超收敛问题

Superconvergence Problem for Nonconforming Finite Element Method

研究了Ｐｏｉｓｓｏｎ方程第一边值问题，给出反例，说明用Ｐ１型非协调元求其近似解，即使区域剖分是一致的，也无插值的第一弱估计，进而说明有限元解无超收敛．

An inverse example is given so as to explain that there are not uniform superconvergence and average superconvergence for derivatives in nodal points although the triangulation is uniform meshes when solving Dirichlet problem of Poisson equation using P1 nonconforming finite element method.