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Journal of Scientific Computing

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22-03-2019

Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction

Authors: Dongfang Li, Chengda Wu, Zhimin Zhang

Published in: Journal of Scientific Computing | Issue 1/2019

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Abstract

A Newton linearized Galerkin finite element method is proposed to solve nonlinear time fractional parabolic problems with non-smooth solutions in time direction. Iterative processes or corrected schemes become dispensable by the use of the Newton linearized method and graded meshes in the temporal direction. The optimal error estimate in the \(L^2\)-norm is obtained without any time step restrictions dependent on the spatial mesh size. Such unconditional convergence results are proved by including the initial time singularity into concern, while previous unconditional convergent results always require continuity and boundedness of the temporal derivative of the exact solution. Numerical experiments are conducted to confirm the theoretical results.

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Title: Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction
Authors: Dongfang Li
Chengda Wu
Zhimin Zhang
Publication date: 22-03-2019
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-00943-0

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