On correlation between the discontinuous Galerkin method and MUSCL-type schemes

The discontinuous Galerkin method is compared with MUSCL-type schemes. Description and analysis of schemes are presented as applied to the linear constant-coefficient advection equation. The techniques for generalizing schemes to nonlinear and multidimensional problems are considered. The distinctive features and correlations between the discontinuous Galerkin method and MUSCL-type schemes are revealed. The accuracy and efficiency criteria of the schemes when applied to different-type problems are discussed.