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**On discontinuous Galerkin methods.**
*(English)*
Zbl 1032.76607

Summary: Discontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present. Several alternatives for treating the diffusion and advective fluxes have been introduced. This report summarizes some of the methods that have been proposed.

Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion-reaction problems and advection-diffusion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method.

Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion-reaction problems and advection-diffusion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76R99 | Diffusion and convection |

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\textit{O. C. Zienkiewicz} et al., Int. J. Numer. Methods Eng. 58, No. 8, 1119--1148 (2003; Zbl 1032.76607)

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