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

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