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A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation

Author

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  • Shi, Xiangyu
  • Lu, Linzhang

Abstract

A new low order two-grid mixed finite element method (FEM) is developed for the nonlinear Benjamin-Bona-Mahoney (BBM) equation, in which the famous nonconforming rectangular CNQ1rot element and Q0 × Q0 constant element are used to approximate the exact solution u and the variable p→=∇ut, respectively. Then, based on the special properties of these two elements and interpolation post-processing technique, the superconvergence results for u in broken H1-norm and p→ in L2-norm are obtained for the semi-discrete and Crank-Nicolson fully-discrete schemes without the restriction between the time step τ and coarse mesh size H or the fine mesh size h, which improve the results of the existing literature. Finally, some numerical results are provided to confirm the theoretical analysis.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:371:y:2020:i:c:s009630031930935x
    DOI: 10.1016/j.amc.2019.124943
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    References listed on IDEAS

    as
    1. 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.
    2. Shi, Dongyang & Wang, Lele & Liao, Xin, 2016. "A new nonconforming mixed finite element scheme for second order eigenvalue problem," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 842-855.
    3. 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.
    4. Shi, Dongyang & Liao, Xin & Wang, Lele, 2016. "Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 298-310.
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