DISCRETE H1-INEQUALITIES FOR SPACES ADMITTING M-DECOMPOSITIONS

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Scopus Citations
Scopus Metrics
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)3407-3429
Journal / PublicationSIAM Journal on Numerical Analysis
Volume56
Issue number6
Online published4 Dec 2018
Publication statusPublished - 2018

Link(s)

DOI

DOI
Check@CityULib
Attachment(s)
Documents
Publisher's Copyright Statement
  • © 2018 Society for Industrial and Applied Mathematics.
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-85060527083&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(f22a4b10-8094-40a8-afc0-d020ac3955e1).html

Abstract

We find new discrete H1- and Poincaré-Friedrichs inequalities by studying the invertibility of the discontinuous Galkerkin (DG) approximation of the flux for local spaces admitting M-decompositions. We then show how to use these inequalities to define and analyze new, superconvergent hybridizable DG (HDG) and mixed methods for which the stabilization function is defined in such a way that the approximations satisfy new H1-stability results with which their error analysis is greatly simplified. We apply this approach to define a wide class of energy-bounded, superconvergent HDG and mixed methods for the incompressible Navier-Stokes equations defined on unstructured meshes using, in two dimensions, general polygonal elements and, in three dimensions, general, flat-faced tetrahedral, prismatic, pyramidal, and hexahedral elements.

Research Area(s)

  • Discontinuous Galerkin, hybridization, stability, superconvergence, Navier-Stokes, DISCONTINUOUS GALERKIN METHODS, HDG METHODS, CONSTRUCTION

Fingerprint

Publication fingerprints text

100
Hybridizable Keyphrases
100
Approximation Mathematics
100
decomposition INIS
100
space INIS
100
hydrogen 1 INIS
66
approximations INIS
66
dimensions INIS
50
Stability Results Keyphrases
50
Local Space Keyphrases
50
Invertibility Keyphrases
Full Fingerprint ›

Citation Format(s)

[ RIS ] [ BibTeX ]
DISCRETE H1-INEQUALITIES FOR SPACES ADMITTING M-DECOMPOSITIONS. / COCKBURN, Bernardo; FU, Guosheng; QIU, Weifeng.
In: SIAM Journal on Numerical Analysis, Vol. 56, No. 6, 2018, p. 3407-3429.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Download Statistics

No data available