Geodesic
On correlation between the discontinuous Galerkin method and MUSCL-type schemes
Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 96-116

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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.
Keywords: Godunov-type schemes, Riemann problem, piecewise-linear approximation, Shu and Osher test problem, double Mach reflection test problem. 
@article{MM_2015_27_10_a7,
     author = {A. V. Rodionov},
     title = {On correlation between the discontinuous {Galerkin} method and {MUSCL-type} schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {96--116},
     publisher = {mathdoc},
     volume = {27},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_10_a7/}
}
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A. V. Rodionov. On correlation between the discontinuous Galerkin method and MUSCL-type schemes. Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 96-116. http://geodesic.mathdoc.fr/item/MM_2015_27_10_a7/