Geodesic
Approximation of discontinuous solutions in high order discontinous Galerkin schemes
Matematičeskoe modelirovanie, Tome 17 (2005) no. 1, pp. 79-92.

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The paper concerns high order discontinuous Galerkin schemes. The numerical solution of ordinary differential equations is considered for those problems where the approximation of a discontinuous solution is required. It will be shown that the high order discontinuous Galerkin approximation results in solution overshoots on a grid cell which contains a discontinuity. For a linear problem, analytical expressions to evaluate the amplitude of the solution overshoot are obtained. Numerical examples confirming the theoretical results are given for both linear and nonlinear problems. 
@article{MM_2005_17_1_a6,
     author = {N. B. Petrovskaya},
     title = {Approximation of discontinuous solutions in high order discontinous {Galerkin} schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {79--92},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_1_a6/}
}
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N. B. Petrovskaya. Approximation of discontinuous solutions in high order discontinous Galerkin schemes. Matematičeskoe modelirovanie, Tome 17 (2005) no. 1, pp. 79-92. http://geodesic.mathdoc.fr/item/MM_2005_17_1_a6/