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Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem

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  • Shi, Dongyang
  • Yang, Huaijun

Abstract

In this paper, we study the superconvergence analysis of nonlinear time-dependent thermistor problem with the well-known nonconforming element, i.e., the extension of the rotated bilinear element (denoted EQ1rot), for the semi-discrete and a linearized backward Euler fully-discrete schemes. The superclose and superconvergent estimates about the related variables in broken H1-norm are derived with the help of the rigorous analysis together with the special properties of this element, mean value technique and interpolated post-processing approach. Finally, a numerical experiment is carried out to confirm the theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Yang, Huaijun, 2019. "Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 210-224.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:210-224
    DOI: 10.1016/j.amc.2018.10.018
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    References listed on IDEAS

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    1. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 216-226.
    2. Shi, Dongyang & Yang, Huaijun, 2018. "Superconvergence analysis of finite element method for time-fractional Thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 31-42.
    3. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 1-16.
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    Cited by:

    1. Shi, Xiangyu & Lu, Linzhang, 2020. "A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).

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