A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows (Advances in Applied Mathematics and Mechanics, 2010)
In this paper, we describe a residual distribution (RD) method where,contrarily to "standard" this type schemes, the mesh is not necessarily conformal. Italso allows using discontinuous elements, contrary to the "standard" case wherecontinuous elements are requested. Moreover, if continuity is forced, the scheme issimilar to the standard RD case. Hence, the situation becomes comparable with theDiscontinuous Galerkin (DG) method, but it is simpler to implement than DG andhas guaranteed $L^∞$ bounds. We focus on the second-order case, but the method canbe easily generalized to higher degree polynomials.