Exponential growth, exponential scaling, and DG

Vaclav Kucera

Department of Numerical Mathematics
Faculty of Mathematics and Physics
Charles University

Gronwall's lemma is a standard tool in the analysis of time-dependent problems. However it takes into account the worst possible case which leads to exponential growth in time of the resulting estimate.  In this talk we demonstrate how to use a simple exponential scaling trick to obtain uniform estimates in time (or other sub-exponential growth rates} in the case of the discontinuous Galerkin method applied to advective problems. The results thus obtained have a surprising interpretation.