几乎不可压缩线性弹性问题的多重网格Uzawa型混合有限元方法

葛志昊,葛媛媛

Multigrid Uzawa-Type Mixed Finite Element Methods for Nearly Incompressible Linear Elasticity Problem

Zhihao Ge,Yuanyuan Ge

表 4.3 ($\lambda=10^{20}$)

$ h $ $ |\vec{u}-\vec{u}_j|_{H^1} $ $|\vec{u}-\vec{u}_j|$ $ \|\vec{u}-\vec{u}_j\| $ $ \|p-p_j\| $ $ \frac{\sqrt{2}}{2^4} $ 0.00990824 0.0112103 0.000289378 0.000981775 $ \frac{\sqrt{2}}{2^5} $ 0.00497386 0.00565981 7.37462$\times10^{-5}$ 0.000255086 $ \frac{\sqrt{2}}{2^6} $ 0.00248929 0.00283681 1.85207$\times10^{-5}$ 6.36543$\times10^{-5}$ $ \frac{\sqrt{2}}{2^7} $ 0.00124493 0.00141927 4.63482$\times10^{-6}$ 1.57971$\times10^{-5}$ $ \frac{\sqrt{2}}{2^8} $ 0.000622503 0.00070974 1.15892$\times10^{-6}$ 3.9281$\times10^{-6}$ 平均误差阶 0.9981 0.9954 1.9910 1.9914