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The Upwind Finite Volume Element Method for Two-Dimensional Time Fractional Coupled Burgers’ Equation

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  • Zechao Lv
  • Qing Yang

Abstract

The finite volume element method for approximating a two-dimensional time fractional coupled Burgers' equation is presented. The linear finite volume element method is used for spatial discretization and the upwind technique is used for the nonlinear convective term to get the semi-discrete scheme. Further, the time-fractional derivative term is approximated by using L1 formula and the nonlinear convection term is treated by linearized upwind technique to get the fully discrete scheme. We prove that the semi-discrete scheme is convergent with one-order accuracy in space and the fully discrete scheme is convergent with one-order accuracy both in time and space in L^2-norm. Numerical experiments are presented finally to validate the theoretical analysis.

Suggested Citation

  • Zechao Lv & Qing Yang, 2024. "The Upwind Finite Volume Element Method for Two-Dimensional Time Fractional Coupled Burgers’ Equation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 16(1), pages 1-31, December.
    • Handle: RePEc:ibn:jmrjnl:v:16:y:2024:i:1:p:31
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    References listed on IDEAS

    as
    1. Sayevand, K. & Arjang, F., 2016. "Finite volume element method and its stability analysis for analyzing the behavior of sub-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 224-239.
    2. Zhang, Yadong & Feng, Minfu, 2023. "A local projection stabilization virtual element method for the time-fractional Burgers equation with high Reynolds numbers," Applied Mathematics and Computation, Elsevier, vol. 436(C).
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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