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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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