A priori error estimates of a local-structure-preserving LDG method

In this note, the missing error estimates in the L norm and in a new energy norm are established for a local-structure-preserving local discontinuous Galerkin method proposed in [F. Li and C.-W. Shu, Methods and Applications of Analysis, v13 (2006), pp.215-233] for the Laplace equation. With its distinctive feature in using harmonic polynomials as local approximations, the method has lower computational complexity than standard discontinuous Galerkin methods. The analysis in this note is based on the primal formulation of the scheme.