Improving the accuracy of LDG approximations on coarse meshes

A realization of an r-adaptive procedure preserving mesh connectivity is analyzed for the Local Discontinuous Galerkin (LDG) method applied to an elliptic problem. The discrete energy functional of the LDG method is locally minimized by considering a set of local variational problems, each one associated to an interior grid node. The algorithm consists of solving small minimization problems, cyclically, using a Gauss–Seidel sweep. The algorithm can be easily applied to high order approximations. The adaptive procedure is validated on a wide variety of one and two dimensional problems using high order approximations.