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
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葛志昊,葛媛媛
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Multigrid Uzawa-Type Mixed Finite Element Methods for Nearly Incompressible Linear Elasticity Problem
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Zhihao Ge,Yuanyuan Ge
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表 4.5
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| $ h $ | $ |\vec{u}-\vec{u}_j| $ | $\|\vec{u}-\vec{u}_j\|$ | $|\vec{u}-\vec{u}_j|_{H^1}$ | $ \|p-p_j\| $ | | MUMFEM | $\sqrt{2}/2^4$ | 0.011224 | 0.000289379 | 0.00991621 | 0.00858243 | | $\sqrt{2}/2^5$ | 0.00567571 | 7.39909$\times10^{-5}$ | 0.00498314 | 0.00919007 | | $\sqrt{2}/2^6$ | 0.00285473 | 1.88377$\times10^{-5}$ | 0.00249968 | 0.00957303 | | $\sqrt{2}/2^7$ | 0.00143837 | 4.97168$\times10^{-6}$ | 0.00125595 | 0.00978083 | | 平均收敛阶 | | 0.9880 | 1.9543 | 0.9937 | | | IMUMFEM | $\sqrt{2}/2^4$ | 0.0112356 | 0.00028971 | 0.00992303 | 0.00609284 | | $\sqrt{2}/2^5$ | 0.00568659 | 7.40819$\times10^{-5}$ | 0.00498939 | 0.0073056 | | $\sqrt{2}/2^6$ | 0.00286445 | 1.90212$\times10^{-5}$ | 0.00250526 | 0.00843153 | | $\sqrt{2}/2^7$ | 0.00144767 | 5.25868$\times10^{-6}$ | 0.00126132 | 0.00915367 | | 平均收敛阶 | | 0.9854 | 1.9279 | 0.9919 | |
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