Characteristic Mixed Finite Element Methods For Fourth Order Equations

Characteristic mixed finite element methods for four order equations are discussed in this paper.The main features of these methods are that the high order equations are lowered by the mixed finite element method firstly.and time derivative is discretized by the charac-teristic method.Then the lower equations are discretized by the continuous finite element methods.For a kind of fourth order parabolic equationsusing mixed finiteψ=△φfor lowering the high order equation,and the characteristic method inφ_t+ u·(?)φof equation are used.The characteristic mixed finite element scheme are given.Existence and uniqueness,stability and error estimates of the finite element solution are proved.For a kind of one dimensional four order equations,using mixed finiteφ= u_t-u_xx for lowering the high order equation, discretized time derivative with Euler method and characteristic method,and discretized space variable us-ing continuous finite element method.Related estimations of the finite element solution are proved.