Correlation between the discontinuous Galerkin method and MUSCL-type schemes

详细

The discontinuous Galerkin method is compared with MUSCL-type schemes. The description and the analysis of the schemes are presented by using the solution of the linear advection equation as an example. The techniques for a generalization of these schemes to the case of solving nonlinear and multidimensional problems are considered. The correlation between the discontinuous Galerkin method and MUSCL-type schemes, as well as their distinctive features, are revealed. The criteria of the accuracy and the efficiency of the schemes as applied to problems of various classes are discussed.