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      Analysis of injection operators in multigrid solvers for hybridized discontinuous Galerkin methods

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          Abstract

          Uniform convergence of the geometric multigrid V-cycle is proven for HDG methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme involves standard smoothers and local solvers which are bounded, convergent, and consistent. Elliptic regularity is used in the proofs. The new assumptions admit injection operators local to a single coarse grid cell. Examples for admissible injection operators are given. The analysis applies to the hybridized local discontinuous Galerkin method, hybridized Raviart-Thomas, and hybridized Brezzi-Douglas-Marini mixed element methods. Numerical experiments are provided to confirm the theoretical results.

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          Author and article information

          Journal
          31 March 2021
          Article
          2104.00118
          5e945390-8d0b-4242-8cc8-8829fff98019

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          65F10, 65N30, 65N50
          arXiv admin note: text overlap with arXiv:2011.14018
          math.NA cs.NA

          Numerical & Computational mathematics
          Numerical & Computational mathematics

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