The Mixed Finite Element Method For Two-kinds Of Burgers Equations

In this paper, we consider the expanded mixed finite element method for the quasi-liner burgers-type equation with the initial-value problemsWe give the semi-discrete expanded mixed finite element scheme, and the uniqueness ofthe solution which satisfies the scheme is proved. It is obtained that the error estimates forunknown function, the flux and the gradient of the unknown function in L2-norms.Then we simulate the following two-dimensional Burgers equation with the initial-value problemsWhich is stimulated by the mixed covolume method. The full-discrete mixed volumeelement format is obtained. The lowest order Raviart-Thomas mixed element space onrectangles is used. The error estimates for the unknown function and the gradient of theunknown function is obtained by the inductional assumption.