Paper Publications
An optimal error estimate for the two-dimensional nonlinear time fractional advection-diffusion equation with smooth and non-smooth solutions
Release Time:2020-07-09
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Institution:
数学学院
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Journal:
Computers & Mathematics with Applications
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Key Words:
Two-dimensional nonlinear time fractional advection-diffusion equation; Linearized L1 Legendre-Galerkin spectral method; Optimal error estimate; Error splitting argument technique; Correction method
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Summary:
In this paper, a linearized L1 Legendre-Galerkin spectral method for the two-dimensional nonlinear time fractional advection-diffusion equation is derived. The numerical method is stable without the CFL conditions based on the error splitting argument technique and the discrete fractional Gronwall type inequality. We also consider the case of non-smooth solutions by adding some correction terms. The numerical experiments are given to verify the theoretical analysis and the effectiveness of the correction method.
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First Author:
张慧
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Correspondence Author:
贾俊青,蒋晓芸
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Discipline:
Natural Science
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First-Level Discipline:
Mathematics
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Volume:
79
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Issue:
10
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Page Number:
2819-2831
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Translation or Not:
No
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Date of Publication:
2020-05
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Included Journals:
SCI
