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 2 当$\alpha=0.15$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 ${t_n}/{2}$ 6.913e-04 / 9.330e-04 / 2.740e-03 / ${t_n}/{4}$ 1.890e-04 1.871 2.537e-04 1.879 7.466e-04 1.876 0.1 ${t_n}/{8}$ 5.174e-05 1.869 6.974e-05 1.863 2.044e-04 1.869 ${t_n}/{16}$ 1.430e-05 1.856 1.9267e-05 1.856 5.649e-05 1.855 ${t_n}/{2}$ 6.845e-05 / 8.960e-05 / 2.832e-04 / ${t_n}/{4}$ 1.881e-05 1.864 2.461e-05 1.864 7.790e-05 1.862 0.01 ${t_n}/{8}$ 5.196e-06 1.856 6.799e-06 1.856 2.153e-05 1.855 ${t_n}/{16}$ 1.440e-06 1.851 1.885e-06 1.851 5.968e-06 1.851