ERROR ESTIMATES FOR APPROXIMATIONS OF DISTRIBUTED ORDER TIME FRACTIONAL DIFFUSION WITH NONSMOOTH DATA

作者：Jin Bangti^*; Lazarov Raytcho^*; Sheen Dongwoo^*; Zhou Zhi^*

来源：Fractional Calculus and Applied Analysis, 2016, 19(1): 69-93.

DOI：10.1515/fca-2016-0005

• distributed order
• fractional diffusion
• Galerkin finite element method
• fully discrete scheme
• error estimates

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 L-2(Omega) and H-1(Omega) 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 L-2(Omega) 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.

• 出版日期2016-2