摘要
利用Wilson元提出了一类二维时间分数阶扩散方程的新的全离散逼近格式.基于单元的性质,在不需要外推和插值后处理技术的前提下,得到了u的比传统的H1-范数更大的模意义下相应的O(h^2+τ^(2-α/2))阶的误差分析结果,正好比通常的关于Wilson元的误差估计高出一阶.这里,h,τ分别表示空间剖分参数和时间步长.
In this paper,with the help of the Wilson element,a new fully-discrete scheme is proposed for two-dimensional time fractional diffusion equations. Based on the properties of the element,the convergence result of order O( h2+τ2-α/2) in the norm which is stronger than the usual H1-norm for the primitive solution u is obtained without using the technique of extrapolation and interpolated post-processing. The above result is just one order higher than the usual error estimates of the Wilson element. Here,h and τ are parameters of the subdivision in space and time step,respectively.
作者
杨晓侠
YANG Xiaoxia(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan,Henan467099,China)
出处
《平顶山学院学报》
2019年第2期1-6,共6页
Journal of Pingdingshan University
基金
河南省科技厅基础与前沿技术研究计划项目(162300410082)
关键词
二维时间分数阶扩散方程
WILSON元
全离散格式
收敛性
two-dimensional time fractional diffusion equations
Wilson element
fully-discrete scheme
convergence
