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

In this paper, the semi-discrete and fully discrete modified weak Galerkin finite element methods 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 modified weak Galerkin finite element method for the quasilinear parabolic problemModified weak Galerkin finite element schemes are presented, existence and unique-ness of their solutions are given. The optimal order error estimations of the L2 norm and the |||·|||w,1 norm of the numerical solutions are proved. Experimental data are given and the error behaviors of the methods are verified.In Chapter two, we consider the quasilinear parabolic inter-differential equationAccording to the first chapter to apply this method to the quasilinear parabolic inter-differential equation. Modified weak Galerkin finite element schemes are pre-sented, existence and uniqueness of their solutions are given. The optimal order error estimations of the L2 norm and the |||·|||w,1 norm of the numerical solutions are proved. Experimental data are given and the error behaviors of the methods are verified.