{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:48:26Z","timestamp":1776833306489,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"327","license":[{"start":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T00:00:00Z","timestamp":1632355200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1818867"],"award-info":[{"award-number":["1818867"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we propose a simple way of constructing HDG+ projections on polyhedral elements. The projections enable us to analyze the Lehrenfeld\u2013Sch\u00f6berl HDG (HDG+) methods in a very concise manner, and make many existing analysis techniques of standard HDG methods reusable for HDG+. The novelty here is an alternative way of constructing the projections without using\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper M\">\n                        <mml:semantics>\n                          <mml:mi>M<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">M<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -decompositions as a middle step. This extends our previous results [S. Du and F.-J. Sayas, SpringerBriefs in Mathematics (2019)] (elliptic problems) and [S. Du and F.-J. Sayas, Math.\u00a0Comp.\u00a089\u00a0(2020), pp. 1745\u20131782] (elasticity) to polyhedral meshes.\n                  <\/p>","DOI":"10.1090\/mcom\/3573","type":"journal-article","created":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T13:19:18Z","timestamp":1597843158000},"page":"65-79","source":"Crossref","is-referenced-by-count":6,"title":["A note on devising HDG+ projections on polyhedral elements"],"prefix":"10.1090","volume":"90","author":[{"given":"Shukai","family":"Du","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco-Javier","family":"Sayas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2020,9,23]]},"reference":[{"key":"1","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387759333","edition":"3"},{"issue":"2","key":"2","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. 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Part I: General theory for HDG methods for diffusion","volume":"86","author":"Cockburn, Bernardo","year":"2017","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s10915-017-0547-z","article-title":"Stormer-Numerov HDG methods for acoustic waves","volume":"75","author":"Cockburn, Bernardo","year":"2018","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"issue":"274","key":"7","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1090\/S0025-5718-2010-02410-X","article-title":"Analysis of HDG methods for Stokes flow","volume":"80","author":"Cockburn, Bernardo","year":"2011","journal-title":"Math. 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Droniou, The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications, Modeling, Simulation and Applications, Springer, Cham, 2020.","DOI":"10.1007\/978-3-030-37203-3"},{"key":"13","series-title":"SpringerBriefs in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-27230-2","volume-title":"An invitation to the theory of the hybridizable discontinuous Galerkin method","author":"Du, Shukai","year":"2019","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030272296"},{"issue":"324","key":"14","doi-asserted-by":"publisher","first-page":"1745","DOI":"10.1090\/mcom\/3499","article-title":"New analytical tools for HDG in elasticity, with applications to elastodynamics","volume":"89","author":"Du, Shukai","year":"2020","journal-title":"Math. 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