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 5 $\|u^n-\Pi_{2h}U^n\|_{1}$取不同$\alpha$时在空间方向的误差和收敛阶

$\alpha$ $h$ $t_{n}=0.2$ 阶 $t_{n}=0.4$ 阶 $t_{n}=0.7$ 阶 $t_{n}=0.9$ 阶 $1/4$ 1.540e-01 / 3.080e-01 / 5.390e-01 / 6.931e-01 / $1/8$ 4.179e-02 1.882 8.357e-02 1.882 1.462e-01 1.882 1.880e-01 1.882 0.3 $1/16$ 1.067e-02 1.970 2.133e-02 1.970 3.733e-02 1.970 4.800e-02 1.970 $1/32$ 2.681e-03 1.992 5.361e-03 1.992 9.383e-03 1.992 1.206e-02 1.992 $1/4$ 1.545e-01 / 3.082e-01 / 5.391e-01 / 6.931e-01 / $1/8$ 4.190e-02 1.882 8.362e-02 1.882 1.462e-01 1.882 1.880e-01 1.882 0.6 $1/16$ 1.069e-02 1.970 2.134e-02 1.970 3.733e-02 1.970 4.780e-02 1.970 $1/32$ 2.687e-03 1.993 5.364e-03 1.992 9.382e-03 1.992 1.206e-02 1.992 $1/4$ 1.557e-01 / 3.088e-01 / 5.391e-01 / 6.931e-01 / $1/8$ 4.221e-02 1.883 8.379e-02 1.882 1.463e-01 1.882 1.880e-01 1.882 0.9 $1/16$ 1.077e-02 1.971 2.138e-02 1.970 3.734e-02 1.970 4.800e-02 1.970 $1/32$ 2.071e-03 1.993 5.374e-03 1.993 9.384e-03 1.992 1.206e-02 1.992