论文摘要
本文主要讨论两类非线性问题的非协调混合有限元方法.首先,将一个低阶Crouzeix-Raviart型非协调矩形元应用于定常的热传导-对流方程,利用Banach不动点定理证明了逼近问题解的存在唯一性,然后利用单元自身的特殊性质,得到了关于速度能量模,压力L2-模和温度H1-半模的最优误差估计.其次,我们将一个新的具有二阶收敛精度的非协调元应用于Navier-Stokes方程和Stokes方程,同样得到了速度能量模和压力L2-模的最优误差估计.最后,我们给出数值算例来验证该单元应用于Navier-Stokes方程和Stokes方程理论分析的有效性.
论文目录
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