The finite volume method for two-dimensional Burgers’ equation

Sheng, Ying; Zhang, Tie

doi:10.1007/s00779-018-1143-4

Cited by 7 publications

(2 citation statements)

References 24 publications

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“…Guo et al [20] proposed a fifth-order FV weighted compact scheme to solve one-dimensional Burgers' equation and gave numerical experiments. Sheng and Zhang [21] proposed an FV method to solve two-dimensional Burgers' equation and obtained the optimal error estimate in the H 1 norm. e aim of this article is to develop mixed finite volume element (MFVE) methods to solve one-dimensional Burger's equation by combining the MFE methods [22][23][24][25] with the finite volume element (FVE) methods [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Fang

et al. 2020

Discrete Dynamics in Nature and Society

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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 L2Ω norm are derived by using the stability results. Finally, numerical results are given to verify the feasibility and effectiveness.

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Section: Introductionmentioning

confidence: 99%

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

Zhao

Fang

et al. 2020

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…Ying Sheng et al have proposed the numerical method for solving the Burgers' equation. This method gave a numerical solution to the two-dimensional Burgers' equation and the optimal error estimate in H1 norm based on the variational formulation of the corresponding finite volume method is obtained [31].…”

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confidence: 99%