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

abstract

• 2016 Diogenes Co., Sofia. 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() and H1() 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() 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.

authors

• Lazarov, Raytcho

published proceedings

• FRACTIONAL CALCULUS AND APPLIED ANALYSIS

author list (cited authors)

• Jin, B., Lazarov, R., Sheen, D., & Zhou, Z.

citation count

• 45

complete list of authors

• Jin, Bangti||Lazarov, Raytcho||Sheen, Dongwoo||Zhou, Zhi

publication date

• January 2016

publisher

• Springer Nature  Publisher

published in

• Journal of Fractional Calculus and Applied Analysis  Journal

keywords

• Distributed Order
• Error Estimates
• Fractional Diffusion
• Fully Discrete Scheme
• Galerkin Finite Element Method

Digital Object Identifier (DOI)

• 10.1515/fca-2016-0005

start page

• 69

end page

• 93

volume

• 19

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1515%2Ffca-2016-0005