Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations

Abstract : We present equilibrated flux a posteriori error estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two-dimensional Poisson problem. Relying on the equilibration by mixed finite element solution of patchwise Neumann problems, the estimates are guaranteed, locally computable, locally efficient, and robust with respect to polynomial degree. Maximal local overestimation is guaranteed as well. Numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous Galerkin scheme.
Document type :
Journal articles
Complete list of metadatas

Cited literature [58 references]  Display  Hide  Download

https://hal.inria.fr/hal-00921583
Contributor : Martin Vohralik <>
Submitted on : Wednesday, July 30, 2014 - 5:25:40 PM
Last modification on : Friday, May 25, 2018 - 12:02:07 PM
Long-term archiving on : Tuesday, November 25, 2014 - 9:11:36 PM

File

a_post_rev_HAL.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Collections

Citation

Alexandre Ern, Martin Vohralík. Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1058-1081. ⟨10.1137/130950100⟩. ⟨hal-00921583v2⟩

Share

Metrics

Record views

468

Files downloads

365