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计算数学  2015 

sine-Gordon方程的最低阶各向异性混合元高精度分析新途径

, PP. 148-161

Keywords: sine-Gordon方程,超逼近性和超收敛,混合有限元新模式,半离散和全离散格式

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Abstract:

在各向异性网格下,针对一类非线性sine-Gordon方程利用最简单的双线性元Q11及Q01×Q10元提出了一个自然满足Brezzi-Babu?ka条件的最低阶混合元新模式.基于Q11元的积分恒等式结果,建立了插值与Ritz投影之间在H1模意义下的超收敛估计,再结合关于Q01×Q10元的高精度分析方法和插值后处理技术,对于半离散和全离散格式,均导出了关于原始变量u和流量p=-▽u分别在H1模和L2模意义下单独利用插值或Ritz投影所无法得到的超逼近性和超收敛结果.最后,我们对其它一些著名单元也进行了分析,进一步验证了所选单元的合理性和独特优势.

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