Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

Abstract : We study extensions of piecewise polynomial data prescribed on faces and possibly in elements of a patch of simplices sharing a vertex. In the H1 setting, we look for functions whose jumps across the faces are prescribed, whereas in the H(div) setting, the normal component jumps and the piecewise divergence are prescribed. We show stability in the sense that the minimizers over piecewise polynomial spaces of the same degree as the data are subordinate in the broken energy norm to the minimizers over the whole broken H and H(div) spaces. Our proofs are constructive and yield constants independent of the polynomial degree. One particular application of these results is in a posteriori error analysis, where the present results justify polynomial-degree-robust efficiency of potential and flux reconstructions.
Document type :
Journal articles
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal.inria.fr/hal-01422204
Contributor : Martin Vohralik <>
Submitted on : Friday, October 4, 2019 - 12:18:08 PM
Last modification on : Friday, November 29, 2019 - 12:59:14 PM

File

robust_HAL.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Alexandre Ern, Martin Vohralík. Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Mathematics of Computation, American Mathematical Society, 2019, ⟨10.1090/mcom/3482⟩. ⟨hal-01422204v4⟩

Share

Metrics

Record views

38

Files downloads

277