This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in [2] based on heuristic arguments, however we provide a rigorous derivation, which justifies the increased order of accuracy. Numerical experiments are carried out.
@article{702750,
title = {A new reconstruction-enhanced discontinuous Galerkin method for time-dependent problems},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2010},
pages = {125-130},
url = {http://dml.mathdoc.fr/item/702750}
}
Kučera, Václav. A new reconstruction-enhanced discontinuous Galerkin method for time-dependent problems, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2010), pp. 125-130. http://gdmltest.u-ga.fr/item/702750/