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Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal\/polyhedral (polytopic) elements, giving rise to prismatic space-time elements. A key feature of the proposed method is the use of space-time elemental polynomial bases of total degree, say $p$, defined in the physical coordinate system, as opposed to standard dG time-stepping methods whereby spatial elemental bases are tensorized with temporal basis functions. This approach leads to a fully discrete $hp$-dG scheme using fewer degrees of freedom for each time step, compared to dG time-stepping schemes employing a tensorized space-time basis, with acceptable deterioration of the approximation properties. A second key feature of the new space-time dG method is the incorporation of very general spatial meshes consisting of possibly polygonal\/polyhedral elements with an arbitrary number of faces. A priori error bounds are shown for the proposed method in various norms. An extensive comparison among the new space-time dG method, the (standard) tensorized space-time dG methods, the classical dG time-stepping, and the conforming finite element method in space is presented in a series of numerical experiments.<\/jats:p>","DOI":"10.1137\/16m1073285","type":"journal-article","created":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T11:32:04Z","timestamp":1500377524000},"page":"A1251-A1279","source":"Crossref","is-referenced-by-count":59,"title":["$hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes"],"prefix":"10.1137","volume":"39","author":[{"given":"Andrea","family":"Cangiani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaonan","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuil H.","family":"Georgoulis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,7,18]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-41640-3_9"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/120877246"},{"key":"atypb3","volume-title":"Multigrid Algorithms for $hp$-Version Interior Penalty Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes, preprint, https:\/\/arxiv.org\/abs\/1412.0913","author":"Antonietti P. 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