时间分数阶扩散方程线性三角形元的高精度分析
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史艳华,张亚东,王芬玲,赵艳敏,王萍莉
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High Accuracy Analysis of Linear Triangular Element for Time Fractional Diffusion Equations
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Yanhua Shi,Yadong Zhang,Fenling Wang,Yanmin Zhao,Pingli Wang
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表 3 $\|u^n-U^n\|_{0}$取不同$\alpha$时在空间方向的误差和收敛阶
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| $\alpha$ | $h$ | $t_{n}=0.2$ | 阶 | $t_{n}=0.4$ | 阶 | $t_{n}=0.7$ | 阶 | $t_{n}=0.9$ | 阶 | | 1/4 | 3.952e-02 | / | 8.084e-02 | / | 1.437e-01 | / | 1.860e-01 | / | | $1/8$ | 1.042e-02 | 1.923 | 2.140e-02 | 1.918 | 3.814e-02 | 1.914 | 4.942e-02 | 1.912 | | 0.3 | $1/16$ | 2.640e-03 | 1.981 | 5.424e-03 | 1.980 | 9.676e-03 | 1.979 | 1.254e-02 | 1.979 | | $1/32$ | 6.622e-04 | 1.995 | 1.361e-03 | 1.995 | 2.428e-03 | 1.995 | 3.146e-03 | 1.995 | | 1/4 | 3.642e-02 | / | 7.756e-02 | / | 1.413e-01 | / | 1.844e-01 | / | | 1/8 | 9.487e-02 | 1.941 | 2.039e-02 | 1.928 | 3.737e-02 | 1.919 | 4.889e-02 | 1.915 | | 0.6 | $1/16$ | 2.395e-03 | 1.986 | 5.158e-03 | 1.983 | 9.471e-03 | 1.980 | 1.240e-02 | 1.979 | | $1/32$ | 6.002e-04 | 1.997 | 1.293e-03 | 1.995 | 2.376e-03 | 1.995 | 3.111e-03 | 1.995 | | $1/4$ | 3.229e-02 | / | 7.331e-02 | / | 1.388e-01 | / | 1.833e-01 | / | | $1/8$ | 8.277e-03 | 1.964 | 1.908e-02 | 1.942 | 3.656e-02 | 1.925 | 4.851e-02 | 1.918 | | 0.9 | $1/16$ | 2.081e-03 | 1.992 | 4.814e-03 | 1.986 | 9.255e-03 | 1.982 | 1.230e-02 | 1.980 | | $1/32$ | 5.209e-04 | 1.998 | 1.206e-03 | 1.997 | 2.321e-03 | 1.996 | 3.084e-03 | 1.995 |
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