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计算数学  2013 

抛物型方程一个新的非协调混合元超收敛性分析及外推

, PP. 337-352

Keywords: 抛物型方程,非协调元,新混合元格式,超收敛,外推

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Abstract:

本文研究了抛物型方程在新混合元格式下的非协调混合有限元方法.在抛弃传统有限元分析的必要工具-Ritz投影算子的前提下,直接利用单元的插值性质,运用高精度分析和对时间t的导数转移技巧,借助于插值后处理技术,分别导出了关于原始变量u的H1-模和通量p=▽u在L2-模下的O(h2)阶超逼近性质和整体超收敛.进一步,通过构造合适的辅助问题,运用Richardson外推格式,得到了具有更高精度O(h3)阶的外推结果.最后,给出了一些数值结果验证了理论分析的正确性.

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