时间分数阶扩散方程线性三角形元的高精度分析

史艳华,张亚东,王芬玲,赵艳敏,王萍莉

High Accuracy Analysis of Linear Triangular Element for Time Fractional Diffusion Equations

Yanhua Shi,Yadong Zhang,Fenling Wang,Yanmin Zhao,Pingli Wang

表 1 当$\alpha=0.85$时在$t_n=0.1, t_n=0.01$处时间方向的误差和收敛阶

$ t_n$ $\tau$ $\|u^n-U^n\|_{0}$ 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