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 1 当α=0.85时在tn=0.1,tn=0.01处时间方向的误差和收敛阶
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tn | τ | ‖ | 阶 | \|I_hu^n-U^n\|_{1} | 阶 | \|u^n-\Pi_{2h}U^n\|_{1} | 阶 | | {t_n}/{2} | 3.869e-03 | / | 4.026e-03 | / | 2.121e-02 | / | | {t_n}/{4} | 1.687e-03 | 1.198 | 1.780e-03 | 1.178 | 9.538e-03 | 1.153 | 0.1 | {t_n}/{8} | 7.486e-04 | 1.172 | 7.959e-04 | 1.161 | 4.292e-03 | 1.152 | | {t_n}/{16} | 3.368e-04 | 1.152 | 3.570e-04 | 1.157 | 1.934e-03 | 1.150 | | {t_n}/{2} | 2.091e-05 | / | 1.294e-05 | / | 1.656e-04 | / | | {t_n}/{4} | 9.240e-06 | 1.178 | 5.780e-06 | 1.163 | 7.369e-05 | 1.168 | 0.01 | {t_n}/{8} | 4.125e-06 | 1.164 | 2.596e-06 | 1.155 | 3.308e-05 | 1.156 | | {t_n}/{16} | 1.855e-06 | 1.153 | 1.169e-06 | 1.151 | 1.490e-05 | 1.150 |
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