Sobolev方程有限元解的超收敛结论

Superconvergence conclusions of finite element methods for Sobolev type equations

本文研究Sobolev方程有限元近似解和真解的Ritz-Sobolev投影之间的超收敛结论.当有限元空间指数k≥2时,得到了二者之间的Lp(2≤p≤∞)模超收敛一阶,W1,p(2≤p<∞)模超收敛二阶,W1,∞模超收敛几乎二阶结果.

The superconvergence conclusions between the finite element approximations and the Ritz-Sobolev projection of the exact solution of Sobolev type equations are investigated. When space index of finite element is k ≥ 2, superconvergence orie order in L^p for 2≤ p≤ ∞, two orders in W^1,p for 2≤ p ≤∞, and almost two orders in W^1,∞ are obtained.