Discontinuous high-order finite-volume/finite-element method for inviscid compressible flows
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The discontinuous, hybrid control-volume/finite-element method merges the desirable conservative properties and intuitive physical formulation of the finite-volume technique, with the capability of local arbitrary high-order accuracy distinctive of the discontinuous finite-element method. This relatively novel scheme has been previously applied to the solution of advection-diffusion problems and the shallow-water equations, and is in the present work extended to the Euler equations. The derivation of the method is presented in the general multi-dimensional case, and selected numerical problems are solved in the one- and two-dimensional case.