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The development and application of the Discontinuous Galerkin (DG) methodhave attracted great attention in computational fluid dynamics (CFD) com-munity in the past decades. The underlying reason for such an intensiveinvestigation is due to favorable properties of the DG method, such as higherorder, compactness, and easy parallelization. However, for the compressibleflow simulations, the DG method is also associated with unfavorable prop-erties, such as the frequent instabilities in non-smooth regions. Due to thefinite element formulation, except the update of the cell averaged conserva-tive flow variable, it becomes rather difficulty to fully understand thephysical mechanism in the DG method for the updates of other degrees of freedomin- side each element. In this short note, based on the linear advectionequation we are going to analyze the DG method in an alternative way. Theresults obtained may be useful for the CFD community for its furtherdevelopment of the DG methods.

An Alternative Analysis of Discontinuous Galerkin Method for Hyperbolic Conservation Law