Weak Galerkin finite element methods for Sobolev equation

We present some numerical schemes based on the weak Galerkin finite element method for one class of Sobolev equations, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. The proposed schemes will be proved to have good numerical stability and high order accuracy when time variable is continuous. Also an optimal error estimate is obtained for the fully discrete scheme. Finally, some numerical results are given to verify our analysis for the scheme.