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

The purpose of the paper is to investigate the convergence of the weak Galerkin finite element method for initial-boundary for the linear parabolic integro-differential equation and the Sobolev problems.In Chapter one,we consider the weak Galerkin finite element method for the following problem Based on the space Sh(j)×Sh(j), weak Galerkin finite element schemes are given existence and uniqueness for weak Galerkin approximations and optimal order es-timates in both H1and L2norms are discussed.Numerical example shows that the method we propose is effective.In Chapter two,we consider the Sobolev equation Weak Galerkin fnite element schemes are given, existence and uniqueness for weakGalerkin approximations are discussed.It is on the basis of the frst chapter toapply this method to the Sobolev equation to explore its efectiveness,and we getthe optimal error estimates fnally.