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

In this paper, the semidiscrete and fully discrete modified weak Galerkin finite element approximation schemes for the initial-boundary value problems of time-dependent convection-diffusion equation and the linear parabolic intergro-differential equation are presented.In Chapter one, we consider the modified weak Galerkin finite element method for the following problem Modified weak Galerkin finite element schemes are given, existence and uniqueness of their solutions are discussed. The error estimations of the|||·|||?,1 norm and the L2 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 linear parabolic intergro-differential problem It is on the basis of the first chapter to apply this method to the linear parabolic intergro-differential equation to explore its effectiveness. The existence and unique-ness of their solutions are discussed. The error estimations of the |||·|||?,1 norm and the L2 norm of the numerical solutions are proved. Experimental data are given and the error behaviors of the methods are verified.