Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Abstract : 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 H1, 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 finite element methods, namely for devising stable local commuting projectors and establishing local-best/global-best equivalences in a priori analysis and in the context of a posteriori error estimation. Unconstrained minimization in H1 and constrained minimization in H(div) have been previously treated in the literature. Along with improvement of the results in the H1 and H(div) cases, our key contribution is the treatment of the H(curl) framework. This enables us to cover the whole De Rham diagram in three space dimensions in a single setting.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.inria.fr/hal-03749682
Contributor : Théophile Chaumont-Frelet Connect in order to contact the contributor
Submitted on : Thursday, August 11, 2022 - 11:15:21 AM
Last modification on : Saturday, August 13, 2022 - 12:13:58 PM

File

chaumontfrelet_vohralik_2022a....
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03749682, version 1
  • ARXIV : 2208.05870

Citation

Théophile Chaumont-Frelet, Martin Vohralík. Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the De Rham complex. 2022. ⟨hal-03749682⟩

Share

Metrics

Record views

88

Files downloads

7