# 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…

## 2 Citations

### $p$-robust equilibrated flux reconstruction in ${\boldsymbol H}(\mathrm{curl})$ based on local minimizations. Application to a posteriori analysis of the curl-curl problem

- Mathematics, Computer ScienceArXiv
- 2021

This work presents a local construction of H (curl)-conforming piecewise polynomials satisfying a prescribed curl constraint, and designs guaranteed, fully computable, constant-free, and polynomial-degree-robust a posteriori error estimates of the Prager–Synge type for N´ed´elec’s element approximations of the curl–curl problem.

### A stable local commuting projector and optimal $hp$ approximation estimates in ${\boldsymbol H}(\mathrm{curl})$

- Mathematics
- 2022

We design an operator from the inﬁnite-dimensional Sobolev space H (curl) to its ﬁnite-dimensional subspace formed by the N´ed´elec piecewise polynomials on a tetrahedral mesh that has the following…

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