p-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation

09/29/2020 ∙ by Lorenzo Botti, et al. ∙ 0

We propose a p-multilevel preconditioner for Hybrid High-Order discretizations (HHO) of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical Discontinuous Galerkin scheme. We specifically investigate how the combination of p-coarsening and static condensation influences the performance of the V-cycle iteration for HHO. Two different static condensation procedures are considered, resulting in global linear systems with a different number of unknowns and non-zero elements. An efficient implementation is proposed where coarse level operators are inherited using L^2-orthogonal projections defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free. The various resolution strategies are thoroughly validated on two- and three-dimensional problems.

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