Multigrid for an HDG method

@article{Cockburn2013MultigridFA,
  title={Multigrid for an HDG method},
  author={Bernardo Cockburn and Olivier Dubois and Jay Gopalakrishnan and S. Tan},
  journal={IMA Journal of Numerical Analysis},
  year={2013},
  volume={34},
  pages={1386-1425}
}
We analyze the convergence of a multigrid algorithm for the Hybridizable Discontinuous Galerkin (HDG) method for diffusion problems. We prove that a non-nested multigrid V-cycle, with a single smoothing step per level, converges at a mesh independent rate. Along the way, we study conditioning of the HDG method, prove new error estimates for it, and identify an abstract class of problems for which a nonnested two-level multigrid cycle with one smoothing step converges even when the prolongation… 

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