In this work, we investigate the performance of $\left\{h-p-hp\right\}$-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 $\left\{h-p\right\}$-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.

在这项工作中，我们调查了 $\left\{H-p-Hp\right\}$-多级预处理器，用于常数系数不连续的椭圆算子的Galerkin（dG）离散化。针对用于不可压缩的流体计算的多级求解策略的最新出版物表明，粘性术语的dG离散化需要临时继承的多级预处理器。因此，我们考虑通过Bassi和Rebay引入的BR2 dG方法离散化的椭圆算子，并将基于团聚的hp粗化与先前引入的hp粗化进行比较$\left\{H-p\right\}$多级策略。数值结果表明，当多项式足够高且网格足够密集时，可以有效利用hp多级预处理器。