{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T03:21:16Z","timestamp":1785900076324,"version":"3.56.0"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"271","license":[{"start":{"date-parts":[[2011,3,18]],"date-time":"2011-03-18T00:00:00Z","timestamp":1300406400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG method applied to a model second-order elliptic problem.<\/p>","DOI":"10.1090\/s0025-5718-10-02334-3","type":"journal-article","created":{"date-parts":[[2010,4,15]],"date-time":"2010-04-15T09:01:02Z","timestamp":1271322062000},"page":"1351-1367","source":"Crossref","is-referenced-by-count":228,"title":["A projection-based error analysis of HDG methods"],"prefix":"10.1090","volume":"79","author":[{"given":"Bernardo","family":"Cockburn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jayadeep","family":"Gopalakrishnan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco-Javier","family":"Sayas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2010,3,18]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1051\/m2an\/1985190100071","article-title":"Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates","volume":"19","author":"Arnold, D. N.","year":"1985","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/S0036142901384162","article-title":"Unified analysis of discontinuous Galerkin methods for elliptic problems","volume":"39","author":"Arnold, Douglas N.","year":"2001","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"3","first-page":"599","article-title":"Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Gelerkin\u2019s and finite difference methods","volume":"21","author":"Aubin, Jean-Pierre","year":"1967","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0391-173X","issn-type":"print"},{"issue":"10","key":"4","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1002\/fld.562","article-title":"Superconvergence and \ud835\udc3b(\ud835\udc51\ud835\udc56\ud835\udc63) projection for discontinuous Galerkin methods","volume":"42","author":"Bastian, Peter","year":"2003","journal-title":"Internat. J. Numer. Methods Fluids","ISSN":"https:\/\/id.crossref.org\/issn\/0271-2091","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/BF01389710","article-title":"Two families of mixed finite elements for second order elliptic problems","volume":"47","author":"Brezzi, Franco","year":"1985","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"257","key":"6","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1090\/S0025-5718-06-01895-3","article-title":"Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension","volume":"76","author":"Celiker, Fatih","year":"2007","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"7","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s10915-007-9130-3","article-title":"An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems","volume":"32","author":"Cockburn, Bernardo","year":"2007","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"issue":"264","key":"9","doi-asserted-by":"publisher","first-page":"1887","DOI":"10.1090\/S0025-5718-08-02123-6","article-title":"A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems","volume":"77","author":"Cockburn, Bernardo","year":"2008","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"252","key":"10","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1090\/S0025-5718-05-01741-2","article-title":"Error analysis of variable degree mixed methods for elliptic problems via hybridization","volume":"74","author":"Cockburn, Bernardo","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","article-title":"Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems","volume":"47","author":"Cockburn, Bernardo","year":"2009","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"265","key":"12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0025-5718-08-02146-7","article-title":"Superconvergent discontinuous Galerkin methods for second-order elliptic problems","volume":"78","author":"Cockburn, Bernardo","year":"2009","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"13","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/S0036142900371544","article-title":"Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids","volume":"39","author":"Cockburn, Bernardo","year":"2001","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"251","key":"14","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1090\/S0025-5718-04-01718-1","article-title":"A locally conservative LDG method for the incompressible Navier-Stokes equations","volume":"74","author":"Cockburn, Bernardo","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"15","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1051\/m2an\/1989230101031","article-title":"Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations","volume":"23","author":"Gastaldi, Lucia","year":"1989","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"key":"16","series-title":"Monographs and Studies in Mathematics","isbn-type":"print","volume-title":"Elliptic problems in nonsmooth domains","volume":"24","author":"Grisvard, P.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0273086472"},{"key":"17","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1007\/BF02166687","article-title":"Ein Kriterium f\u00fcr die Quasi-Optimalit\u00e4t des Ritzschen Verfahrens","volume":"11","author":"Nitsche, J.","year":"1968","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"18","first-page":"292","article-title":"A mixed finite element method for 2nd order elliptic problems","author":"Raviart, P.-A.","year":"1977"},{"issue":"5","key":"19","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/BF01397550","article-title":"A family of mixed finite elements for the elasticity problem","volume":"53","author":"Stenberg, Rolf","year":"1988","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"20","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1051\/m2an\/1991250101511","article-title":"Postprocessing schemes for some mixed finite elements","volume":"25","author":"Stenberg, Rolf","year":"1991","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2010-79-271\/S0025-5718-10-02334-3\/S0025-5718-10-02334-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2010-79-271\/S0025-5718-10-02334-3\/S0025-5718-10-02334-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:28:09Z","timestamp":1776788889000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2010-79-271\/S0025-5718-10-02334-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,18]]},"references-count":20,"journal-issue":{"issue":"271","published-print":{"date-parts":[[2010,7]]}},"alternative-id":["S0025-5718-10-02334-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-10-02334-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2010,3,18]]}}}