p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation

We propose a p-multilevel preconditioner for hybrid high-order(HHO)discretizations of the Stokes equation,numerically assess its performance on two variants of the method,and compare with a classical discontinuous Galerkin scheme.An efficient implementa-tion is proposed where coarse level operators are inherited using L2-orthogonal projec-tions defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free.Both h-and k-dependency are investigated tackling two-and three-dimensional problems on standard meshes and graded meshes.For the two HHO for-mulations,featuring discontinuous or hybrid pressure,we study how the combination of p-coarsening and static condensation influences the V-cycle iteration.In particular,two dif-ferent static condensation procedures are considered for the discontinuous pressure HHO variant,resulting in global linear systems with a different number of unknowns and matrix non-zero entries.Interestingly,we show that the efficiency of the solution strategy might be impacted by static condensation options in the case of graded meshes.