Higher-order reconstruction: from finite volumes to discontinuous Galerkin

Abstrakt

This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We follow the methodology of higher order finite volume (FV) and spectral volume (SV) schemes and introduce a reconstruction operator into the discontinuous Galerkin (DG) method.

This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. We present two variants, the generalization of standard FV schemes, already proposed by Dumbser et al. (2008) and the generalization of the SV method.

Theoretical aspects are discussed and numerical experiments are carried out.

Klíčová slova

• higher-order reconstruction
• finite volume method
• spectral volume method
• discontinuous Galerkin method