Show simple item record

dc.contributor.authorCockburn, Bernardo
dc.contributor.authorGopalakrishnan, Jayadeep
dc.contributor.authorNguyen, Ngoc Cuong
dc.contributor.authorPeraire, Jaime
dc.contributor.authorSayas, Francisco-Javier
dc.date.accessioned2011-12-14T20:05:45Z
dc.date.available2011-12-14T20:05:45Z
dc.date.issued2010-09
dc.date.submitted2010-01
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.urihttp://hdl.handle.net/1721.1/67680
dc.description.abstractIn this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree $ k$ for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges. As a consequence, we prove that the approximations of the velocity gradient, the velocity and the pressure converge with the optimal order of convergence of $ k+1$ in $ L[superscript 2]$ for any $ k [greater than or equal to] 0$. Moreover, taking advantage of the superconvergence properties of the velocity, we introduce a new element-by-element postprocessing to obtain a new velocity approximation which is exactly divergence-free, $ \mathbf{H}($div$ )$-conforming, and converges with order $ k+2$ for $ k[greater than or equal to]1$ and with order $ 1$ for $ k=0$. Numerical experiments are presented which validate the theoretical results.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant DMS-0713833)en_US
dc.description.sponsorshipSingapore-MIT Alliance for Research and Technologyen_US
dc.description.sponsorshipUniversity of Minnesota. Supercomputer Instituteen_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant SCREMS-0619080)en_US
dc.description.sponsorshipSpain. Ministerio de Educación y Ciencia (MEC/FEDER Project MTM2007–63204)en_US
dc.description.sponsorshipAragon (Spain) (Grupo PDIE)en_US
dc.language.isoen_US
dc.publisherAmerican Mathematical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1090/S0025-5718-2010-02410-Xen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceAMSen_US
dc.titleAnalysis of HDG Methods for Stokes Flowen_US
dc.typeArticleen_US
dc.identifier.citationCockburn, Bernardo et al. “Analysis of HDG methods for Stokes flow.” Mathematics of Computation 80.274 (2011): 723-723.© 2011 American Mathematical Society.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.contributor.approverPeraire, Jaime
dc.contributor.mitauthorPeraire, Jaime
dc.contributor.mitauthorNguyen, Ngoc Cuong
dc.relation.journalMathematics of Computationen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsCockburn, Bernardo; Gopalakrishnan, Jayadeep; Nguyen, Ngoc Cuong; Peraire, Jaume; Sayas, Francisco-Javieren
dc.identifier.orcidhttps://orcid.org/0000-0002-8556-685X
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record