Abstract: The mixed covolume method for the regularized long wave equation is developed and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.

Key words: multilayer dynamics of fluids, moving boundary values, characteristic finite difference, error estimates, numerical simulation, oil deposit, regularized long wave equation, mixed covolume method, fully discrete, optimal error estimate