Application of reconstruction operators in the discontinuous Galerkin method

Abstract

This paper gives an overview of the main ingredients needed to incorporate reconstruction operators, as known from higher order finite volume (FV) and spectral volume (SV) schemes, into the discontinuous Galerkin (DG) method. Such an operator constructs higher order approximations from the lower order DG scheme, increasing the order of convergence, while leading to a more efficient numerical scheme than the corresponding higher order DG scheme itself.

We discuss theoretical, as well as implementational aspects and numerical experiments.

Keywords

• reconstruction operators
• discontinuous Galerkin method