Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
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DOI：
10.1515/fca-2016-0005
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发表时间：
2015-04
影响因子：
3
通讯作者：
Bangti Jin;R. Lazarov;D. Sheen;Zhi Zhou
中科院分区：
文献类型：
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作者：
Bangti Jin;R. Lazarov;D. Sheen;Zhi Zhou
摘要本文研究了在超慢扩散过程建模中出现的分布阶次扩散模型的数值解。基于Galerkin有限元方法建立了一个空间半离散格式，并对光滑和非光滑初始数据建立了L2（Ω）和H1（Ω）范数下关于数据正则性的最优误差估计.进一步，我们分别基于后向欧拉方法产生的拉普拉斯变换和卷积求积，提出了两种全离散格式，并给出了最优的L2（Ω）误差估计，它们分别具有指数收敛性和一阶收敛性.大量的数值实验提供了光滑和非光滑初始数据的误差估计进行验证。
Abstract In this work, we consider the numerical solution of a distributed order subdiffusion model, arising in the modeling of ultra-slow diffusion processes. We develop a space semidiscrete scheme based on the Galerkin finite element method, and establish error estimates optimal with respect to data regularity in L2(Ω) and H1(Ω) norms for both smooth and nonsmooth initial data. Further, we propose two fully discrete schemes, based on the Laplace transform and convolution quadrature generated by the backward Euler method, respectively, and provide optimal L2(Ω) error estimates, which exhibits exponential convergence and first-order convergence in time, respectively. Extensive numerical experiments are provided to verify the error estimates for both smooth and nonsmooth initial data.