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Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods

Author

Listed:
  • Jie Zhao
  • Hong Li
  • Zhichao Fang
  • Xue Bai

Abstract

In this article, mixed finite volume element (MFVE) methods are proposed for solving the numerical solution of Burgers’ equation. By introducing a transfer operator, semidiscrete and fully discrete MFVE schemes are constructed. The existence, uniqueness, and stability analyses for semidiscrete and fully discrete MFVE schemes are given in detail. The optimal a priori error estimates for the unknown and auxiliary variables in the norm are derived by using the stability results. Finally, numerical results are given to verify the feasibility and effectiveness.

Suggested Citation

  • Jie Zhao & Hong Li & Zhichao Fang & Xue Bai, 2020. "Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-13, March.
    • Handle: RePEc:hin:jnddns:6321209
    DOI: 10.1155/2020/6321209
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    Cited by:

    1. Rawani, Mukesh Kumar & Verma, Amit Kumar & Verma, Lajja, 2024. "Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme," Applied Mathematics and Computation, Elsevier, vol. 467(C).

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