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Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations

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Abstract

In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element method for semilinear parabolic equations. With the error splitting technique and elliptic projection, the optimal error estimates in L2-norm and the discrete H1-norm are derived without any restriction on the time stepsize. Numerical results on both polygonal and tetrahedral meshes are provided to illustrate our theoretical conclusions.

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Acknowledgements

The authors thank the referees for their value comments on the original manuscript, which improve this paper greatly. The authors also thank Gang Wang and Mengyao Wu for providing the uniform polygonal meshes.

Funding

This research is supported by the National Natural Science Foundation of China (No.11971386) and the National Key R&D Program of China(No.2020YFA0713603).

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Authors and Affiliations

  1. Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, China

    Ying Liu, Zhen Guan & Yufeng Nie

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  1. Ying Liu
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  2. Zhen Guan
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  3. Yufeng Nie
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Correspondence to Yufeng Nie.

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Communicated by: Paul Houston

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Liu, Y., Guan, Z. & Nie, Y. Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations. Adv Comput Math 48, 47 (2022). https://doi.org/10.1007/s10444-022-09961-3

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