{h-p-hp}-Multilevel discontinuous Galerkin solution strategies for elliptic operators

In this work, we investigate the performance of h−p−hp-multilevel preconditioners for discontinuous Galerkin (dG) discretisations of elliptic operators with constant coefficients. Recent publications targeting multilevel solution strategies for incompressible fluid flow computations demonstrated that dG discretisation of viscous terms require ad hoc inherited multilevel preconditioners. Accordingly, we consider elliptic operators discretised by means of the BR2 dG method introduced by Bassi and Rebay and we compare agglomeration-based hp-coarsening with previously introduced h−p-multilevel strategies. The numerical results show that, when the polynomial degree is sufficiently high and the mesh is sufficiently dense, the hp-multilevel preconditioner can be fruitfully exploited.