A note on the numerical dissipation from high-order discontinuous finite element schemes

This paper analyzes in detail the numerical dissipation term embedded in high-order discontinuous finite element type discretizations with particular emphasis on numerical schemes that can be formulated from the flux reconstruction methodology (for instance the spectral difference or the nodal discontinuous Galerkin schemes). By introducing the error estimate for the polynomial reconstruction of the solution, an analytical expression is given for the numerical dissipation term arising from using a Lax-Friedrichs type (Toro, 2009) numerical flux at the element interfaces. It is shown that, although some fundamental differences exist in the numerical dissipation term when odd or even numbers of solution points (respectively, even or odd polynomial orders) are used to represent the solution in the element, the overall expected accuracy of the scheme is fully recovered. (C) 2014 Elsevier Ltd. All rights reserved.