{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T04:03:55Z","timestamp":1777003435935,"version":"3.51.4"},"reference-count":100,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,25]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive <jats:italic>a priori<\/jats:italic> error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal <jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.<\/jats:p>","DOI":"10.1515\/jnma-2019-0027","type":"journal-article","created":{"date-parts":[[2019,9,8]],"date-time":"2019-09-08T09:02:30Z","timestamp":1567933350000},"page":"161-174","source":"Crossref","is-referenced-by-count":4,"title":["Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems"],"prefix":"10.1515","volume":"28","author":[{"given":"Maurice S.","family":"Fabien","sequence":"first","affiliation":[{"name":"Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA"}]},{"given":"Matthew G.","family":"Knepley","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, New York, 14260, USA"}]},{"given":"Beatrice M.","family":"Riviere","sequence":"additional","affiliation":[{"name":"Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA"}]}],"member":"374","reference":[{"key":"ref421","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1142\/S0218202513500826","article-title":"Penalty-free discontinuous Galerkin methods for incompressible Navier\u2013Stokes equations","volume":"24","year":"2014","journal-title":"Math. 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