Homogeneous multigrid method for hybridizable interior penalty method

In this paper, we present a rigorous convergence analysis of a homogeneous multigrid method for the hybridizable interior penalty (IP-H) method. In particular, we use the injection operator developed in (Lu et al. SIAM J. Numer. Anal. 60, 2293–2317 2022). It is shown that when the penalization parameter is sufficiently large, our proposed multigrid method is optimal under the assumption of elliptic regularity. Numerical experiments are provided to confirm the theoretical results.