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A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids

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  • Li, Xiaoli
  • Rui, Hongxing

Abstract

In this article, a block-centered finite difference method for the nonlinear Sobolev equation is introduced and analyzed. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with superconvergence O(Δt+h2+k2) for scalar unknown p, its gradient u and its flux q are established on nonuniform rectangular grids, where Δt, h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

Suggested Citation

  • Li, Xiaoli & Rui, Hongxing, 2019. "A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:30
    DOI: 10.1016/j.amc.2019.124607
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    References listed on IDEAS

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    1. Shi, Dongyang & Tang, Qili & Gong, Wei, 2015. "A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 25-36.
    2. Dongyang, Shi & Fengna, Yan & Junjun, Wang, 2016. "Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 182-194.
    3. Tongjun Sun, 2012. "A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, December.
    4. Zhaojie Zhou & Weiwei Wang & Huanzhen Chen, 2013. "An -Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, November.
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    Cited by:

    1. Zhao, Zhihui & Li, Hong & Wang, Jing, 2021. "The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 401(C).

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