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Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations

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Abstract

In this paper, we prove a discrete embedding inequality for the Raviart–Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the proved discrete embedding inequality, we provide an optimal error estimate for linearized mixed finite element methods for nonlinear parabolic equations. Several numerical examples are provided to confirm the theoretical analysis.

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Acknowledgements

The authors would like to thank Prof. Weiwei Sun for useful discussions.

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Correspondence to Weifeng Qiu.

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The work of the Huadong Gao was supported in part by a grant from the National Natural Science Foundation of China (NSFC) under Grant No. 11501227.

The work of the Weifeng Qiu was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China. (Project No. CityU 11302014).

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Gao, H., Qiu, W. Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations. J Sci Comput 77, 1660–1678 (2018). https://doi.org/10.1007/s10915-018-0643-8

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  • DOI: https://doi.org/10.1007/s10915-018-0643-8

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