  A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem
is developed and analyzed in this paper. The DG finite element discretizations
are established, and the corresponding existence and uniqueness theorem is
proved by using Brouwer's fixed point method. Some optimal priori error
estimates under both DG norm and $L^2$ norm are presented. Numerical results
are also shown to confirm the efficiency of the proposed approach.
