Computational aspects of the local discontinuous Galerkin method on unstructured grids in three dimensions

Using tensor notation, a simplified description of the most relevant operators of the local discontinuous Galerkin (LDG) method applied to a general elliptic boundary value problem on unstructured meshes in three dimensions is presented. A reduction of storage is achieved by introducing a fast algorithm for the assembly of the Schur complement. A semi-algebraic multilevel preconditioner for low-order approximations using the classical Lagrange interpolatory basis is discussed. A series of numerical experiments is presented to illustrate the performance of the proposed preconditioning technique and accuracy of the method on three-dimensional problems.