时间分数阶扩散方程线性三角形元的高精度分析

Processing math: 26%

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