A Cubic Finite Volume Element Method for the Burgers Equation

In this paper, for the initial boundary value problem of the Burgers equation, the optimal stress point is used to construct a dual partition, and based on the trial function space of piecewise cubic Lagrange interpolation and the test function space of piecewise constant, the Crank-Nicolson cubic finite volume element scheme is constructed. And the L 2 norm optimal order error estimate of the numerical solutions and the super-convergence error estimate of the derivative at the optimal stress node are proved. Finally, numerical examples are given to verify the theoretical analysis results and the validity of the proposed scheme.