A review of the Local Discontinuous Galerkin (LDG) method applied to elliptic problems

This paper presents a review of the so-called Local Discontinuous Galerkin (LDG) method applied to elliptic problems. The method is presented using a mixed formulation similar to that of the classical mixed finite element method. A summary of the convergence properties is presented. Preliminary theoretical results on super-convergent points are discussed. Numerical experiments of a gradient recovering technique are presented.