High order discontinuous finite-volume/finite-element method for CFD applications

Abstract

The proposed method naturally merges the desirable conservative properties and intuitive physical formulation of the widely used finite-volume (FV) technique, with the capability of local arbitrary high-order accuracy and high-resolution which is distinctive in the discontinuous finite-element (FE) framework. This relatively novel scheme, the discontinuous hybrid control-volume/finite-element method (DCVFEM), has been already applied to the solution of advection-diffusion problems and shallow-water equations, and is in this paper extended to the Euler equations in the one-dimensional case. The main features are summarized and the scheme is compared to the well established FV and discontinuous Galerkin (DG) methods.