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 4 $\|U^n-I_hu^n\|_{1}$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 | | $1/4$ | 5.310e-02 | / | 1.103e-01 | / | 1.982e-01 | / | 2.575e-01 | / | | $1/8$ | 1.387e-02 | 1.937 | 2.894e-02 | 1.930 | 5.217e-02 | 1.925 | 6.790e-02 | 1.923 | | 0.3 | $1/16$ | 3.506e-03 | 1.984 | 7.324e-03 | 1.982 | 1.321e-02 | 1.981 | 1.720e-02 | 1.981 | | $1/32$ | 8.791e-04 | 1.995 | 1.837e-03 | 1.996 | 3.315e-03 | 1.995 | 4.316e-03 | 1.995 | | $1/4$ | 4.606e-02 | / | 1.028e-01 | / | 1.926e-01 | / | 2.538e-01 | / | | $1/8$ | 1.183e-02 | 1.961 | 2.673e-02 | 1.944 | 5.048e-02 | 1.932 | 6.676e-02 | 1.927 | | 0.6 | $1/16$ | 2.977e-03 | 1.990 | 6.749e-03 | 1.986 | 1.277e-02 | 1.983 | 1.690e-02 | 1.982 | | $1/32$ | 7.457e-04 | 1.997 | 1.691e-03 | 1.996 | 3.202e-03 | 1.996 | 4.240e-03 | 1.995 | | $1/4$ | 3.674e-02 | / | 9.320e-02 | / | 1.870e-01 | / | 2.514e-01 | / | | $1/8$ | 9.223e-03 | 1.994 | 2.389e-02 | 1.964 | 4.872e-02 | 1.940 | 6.593e-02 | 1.931 | | 0.9 | $1/16$ | 2.311e-03 | 1.997 | 6.012e-03 | 1.991 | 1.231e-02 | 1.985 | 1.668e-02 | 1.983 | | $1/32$ | 5.781e-04 | 1.999 | 1.505e-03 | 1.998 | 3.085e-03 | 1.996 | 4.182e-03 | 1.996 |
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