一类具有强阻尼Sine-Gordon方程异性网格上的超收敛分析

Superconvergence Analysis for a Class of Sine-Gordon Equations with Strong Damping on Anisotropic Meshes

在异性网格下,利用双二次有限元逼近对一类具有强阻尼Sine-Gordon方程半离散格式进行了收敛性分析。同时,利用插值算子与Ritz投影相一致的性质给出了超逼近性质。最后,通过使用插值后处理技巧得到了它的整体超收敛结果。

The aim of this paper is to study the convergence analysis for a class of Sine-Gordon equations with strong damping by parabolic element under anisotropic meshes. Result of superclose about the nerve transmission signal can be acquired by virtue of the property that the interpolated operator is accordance with the Ritz projection. Finally, the corresponding global superconvergence is got by taking the advantage of the technique of the post-processing operator.