Mixed Finite Volume Element Method For4-order Semi-linear Evolution Equations

Firstly, we consider the mixed fnite volume method for the following4-ordersemi-linear evolution equations with initial and boundary conditionsWe give the semi-discrete and full-discrete mixed fnite volume element scheme basedon triangle mesh, and obtain the optimal error estimates for unknown function in H1-norms and the error estimates for vorticity in L2-norms by introducing the ellipticprojection.Secondly, we consider the following4-order semi-linear evolution equation group(a)ut+△2u=|v|p,(x, t)∈×(0, T],We discuss its semi-discrete and full-discrete mixed fnite volume element schemesfor the coupling of the two equations, and obtain the optimal error estimates forthe two unknown functions in H1-norms, and the error estimates for vorticity in L2-norms respectively.Finally, we present the numerical results which illustrate the efectiveness of the mixed fnite volume element method to solve the problems of this article andobtain the numerical simulation of the equations.