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Nonuniform Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Parabolic Equations

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Abstract

The solutions of the nonlinear time fractional parabolic problems usually undergo dramatic changes at the beginning. In order to overcome the initial singularity, the temporal discretization is done by using the Alikhanov schemes on the nonuniform meshes. And the spatial discretization is achieved by using the finite element methods. The optimal error estimates of the fully discrete schemes hold without certain time-step restrictions dependent on the spatial mesh sizes. Such unconditionally optimal convergent results are proved by taking the global behavior of the analytical solutions into account. Numerical results are presented to confirm the theoretical findings.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Boya Zhou, Xiaoli Chen & Dongfang Li

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Dongfang Li

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  1. Boya Zhou
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  2. Xiaoli Chen
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  3. Dongfang Li
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Correspondence to Dongfang Li.

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This work is supported by NSFC (Grant Nos. 11771162, 11971010).

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Zhou, B., Chen, X. & Li, D. Nonuniform Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Parabolic Equations. J Sci Comput 85, 39 (2020). https://doi.org/10.1007/s10915-020-01350-6

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  • DOI: https://doi.org/10.1007/s10915-020-01350-6

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