On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method

The accuracy in negative-order norms is examined for a local-structure-preserving local discontinuous Galerkin method for the Laplace equation [Li and Shu, Methods and Applications of Analysis, v13 (2006), pp.215-233]. With its distinctive feature in using harmonic polynomials as local approximating functions, this method has lower computational complexity than the standard local discontinuous Galerkin method while keeping the same order of accuracy in both the energy and the L norms. In this note, numerical experiments are presented to demonstrate some accuracy loss of the method in negative-order norms.