Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex

@article{ChaumontFrelet2022ConstrainedAU,
  title={Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex},
  author={Th{\'e}ophile Chaumont-Frelet and Martin Vohral{\'i}k},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.05870}
}
. We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p . We show that the discrete minimizers in the spaces of piecewise polynomials of degree p conforming in the H 1 , H ( curl ), or H (div) spaces are as good as the minimizers in these entire (infinite-dimensional) Sobolev spaces, up to a constant that is independent of p . These results are useful in the analysis and design of… 

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