一类非线性广义神经传播方程非协调元超收敛分析

Superconvergence Analysis of Nonconforming Finite Element to the Generalized Nerve Conductive Equations with Varying Coefficients

讨论了变系数广义神经传播方程在半离散格式下的一类非协调有限元逼近,利用平均值技巧、单元的正交性及相容误差比插值误差高一阶的性质,得到了最优的误差估计和超逼近结果,进一步地,通过插值后处理技术得到了整体超收敛结果.

A kind of nonconforming finite element approximation to the generalized nerve conductive equations with varying coefficients is discussed for semidiscrete scheme. The corresponding optimal error estimates and superclose property are derived by the use of the mean-value technology, orthogonality and one order higher estimate of the consistency error than the interpolation error. Furthermore, the global superconvergence is obtained through in- terpolation postprocessing technique.