Numerical Simulation Of The Weak Galerkin Finite Element Method For Two Kinds Of Quasilinear Evolution Equations

In this paper,the semidiscrete and fully discrete weak Galerkin finite element method for the initial-boundary value problems of the quasilinear parabolic problem and the quasilinear parabolic inter-differential equation are presented.The optimal order error estimates are established.In Chapter one,we consider the weak Galerkin finite element method for the following problem Based on the space Sh(j,l)× Sh(j,l),weak Galerkin finite element schemes are presents,existence and uniqueness for their solutions are discussed.Weak Galerkin elliptic projection is build and the optimal order estimates in both L2 and H1 norms are proved.Experimental datas shows that the method is effective.In Chapter two,we consider the quasilinear parabolic inter-differential equation This chapter is on the basis of the first chapter to apply this method to the quasi-linear parabolic inter-differential equations.Weak Galerkin finite element schemes are given,existence and uniqueness of their solutions are discussed.Generalized weak Galerkin elliptic projection is build and the optimal order error estimates are estab-lished for the corresponding numerical solutions in both L2 and H1 norms.Numerical experiments prove the feasibility of the method.