Mixed Finite Volume Element Method For 4-Order Semi-Linear Parabolic Equations And Its Numerical Simulation

In this paper,we consider the mixed finite volume element method for the 4-order semi-linear parabolic equations with the initial-value problems, and obtained the error estimates of semi-discrete and fully discrete solutions.In Chapter one, we consider the mixed covolume method for the following 4-order semi-linear parabolic equationWe give the mixed finite covolume element scheme for the 4-order semi-linear parabolic equation, and obtained the optimal error estimates for unknown function in H~1-norms, and the error estimates for vorticity in L~2-norms by instructing the elliptic projection.In Chapter two, we consider the following 4-order semi-linear parabolic equation groupWe discuss its semi-discrete and fully-discrete mixed finite covolume element scheme for the coupling of the tuo equations, and obtained the optimal error estimates for unknown function in H~1-norms , and the error estimates for vorticity in L~2-norms respectively. In Chapter three, we present numerical results which illustrate the effectiveness of the mixed finite covolume element method.