(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretization is first established, then the corresponding well-posedness is provided by using Brouwer’s fixed point method. Some optimal priori error estimates under both DG norm and L^2 norm are presented, respectively. Numerical results are given to illustrate the efficiency of the proposed approach.