{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:46Z","timestamp":1787329306539,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are assumed only to be shape regular but may have hanging nodes subject to certain mild grading conditions. A key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a nonconforming subspace that is controlled by the jumps across the edges.<\/jats:p>","DOI":"10.1137\/07069691x","type":"journal-article","created":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T14:11:44Z","timestamp":1215699104000},"page":"2742-2768","source":"Crossref","is-referenced-by-count":19,"title":["A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method"],"prefix":"10.1137","volume":"46","author":[{"given":"Kolja","family":"Brix","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin Campos","family":"Pinto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Dahmen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,7,3]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0719052"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1990-1023042-6"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00746-6"},{"key":"R5","unstructured":"K. Brix, M. Campos Pinto, W. Dahmen, and R. Massjung,\n                      Multilevel preconditioners for the interior penalty discontinuous Galerkin method\n                      II -\n                      Quantitative Studies\n                      , IGPM report 282, RWTH-Aachen, 2007, Commun. Comput. Phys., to appear."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(82)90060-0"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002713"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385864"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"P. Deuflhard and A. Hohmann,\n                      Numerical Analysis in Modern Scientific Computing. An Introduction\n                      , Texts Appl. 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Houston,\n                      $hp$-DGFEM for partial differential equations with nonnegative characteristic form\n                      , in Discontinuous Galerkin Methods: Theory, Computation and Applications, Lect. Notes Comput. Sci.  Eng. 11, B. Cockburn, G. E. Karniadakis, and C.W. 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