【摘要】 讨论了Sine-Gordon方程的二重网格有限元方法，建立了EQ^rot₁非协调元全离散逼近格式.直接利用EQ^rot₁元的插值算子和该元的性质，并对非线性项进行线性化处理，导出了能量模意义下的超逼近结果.更进一步利用插值后处理技术得到整体超收敛结果.更多还原

【Abstract】 This article discusses the two-grid finite element method for the Sine-Gordon equation and establishes a fully discrete approximation scheme for EQ^rot₁nonconforming element. By directly utilizing the interpolation operator of the EQ^rot₁element and its properties, as well as linearizing the nonlinear term, the superclose result in the sense of energy mode is derived. Further, the global superconvergence result is obtained by interpolation postprocessing technique.更多还原