Entropy Inequality for High Order Discontinuous Galerkin Approximation of Euler Equations

This paper is devoted to the presentation of a new family of high order numerical schemes in space (first order in time) for the numerical solution of the Euler equations. We restrict the presentation to the 1D case. Full extention to the multi-dimensional case is discussed in [9] with complete discussion of the entropy properties and some numerical simulations. See [8] for an elementary discussion of the entropy inequality.

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