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Stability and convergence of a fully discrete local discontinuous Galerkin method for multi-term time fractional diffusion equations

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Abstract

In this paper, a fully discrete local discontinuous Galerkin method for a class of multi-term time fractional diffusion equations is proposed and analyzed. Using local discontinuous Galerkin method in spatial direction and classical L1 approximation in temporal direction, a fully discrete scheme is established. By choosing the numerical flux carefully, we prove that the method is unconditionally stable and convergent with order O(h k+1 + (Δt)2−α), where k, h, and Δt are the degree of piecewise polynomial, the space, and time step sizes, respectively. Numerical examples are carried out to illustrate the effectiveness of the numerical scheme.

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Authors and Affiliations

  1. College of Science, Henan University of Technology, Zhengzhou, Henan, 450001, People’s Republic of China

    Leilei Wei

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  1. Leilei Wei
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Correspondence to Leilei Wei.

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This work is supported by the High-Level Personal Foundation of Henan University of Technology (2013BS041), Plan For Scientific Innovation Talent of Henan University of Technology (2013CXRC12), the National Natural Science Foundation of China (11461072,11601124), Foundation of Henan Educational Committee (15A110015,15A110018), and China Postdoctoral Science Foundation funded project (2015M572115).

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Wei, L. Stability and convergence of a fully discrete local discontinuous Galerkin method for multi-term time fractional diffusion equations. Numer Algor 76, 695–707 (2017). https://doi.org/10.1007/s11075-017-0277-1

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  • DOI: https://doi.org/10.1007/s11075-017-0277-1

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