Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 19, Issue 1, Pages 69-93Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2016-0005
Keywords
distributed order; fractional diffusion; Galerkin finite element method; fully discrete scheme; error estimates
Funding
- UK EPSRC [EP/M025160/1]
- NSF [DMS-1016525]
- [NRF-2014R1A2A1A11052429]
- National Research Foundation of Korea [2014R1A2A1A11052429] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
- Engineering and Physical Sciences Research Council [EP/M025160/1] Funding Source: researchfish
- EPSRC [EP/M025160/1] Funding Source: UKRI
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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.
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