{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:38:51Z","timestamp":1773391131656,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,6,23]],"date-time":"2010-06-23T00:00:00Z","timestamp":1277251200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2011,1]]},"DOI":"10.1007\/s10915-010-9390-1","type":"journal-article","created":{"date-parts":[[2010,6,22]],"date-time":"2010-06-22T10:49:33Z","timestamp":1277203773000},"page":"124-149","source":"Crossref","is-referenced-by-count":53,"title":["A Class of Domain Decomposition Preconditioners for\u00a0hp-Discontinuous Galerkin Finite Element Methods"],"prefix":"10.1007","volume":"46","author":[{"given":"Paola F.","family":"Antonietti","sequence":"first","affiliation":[]},{"given":"Paul","family":"Houston","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,6,23]]},"reference":[{"key":"9390_CR1","series-title":"Pure and Applied Mathematics","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. Pure and Applied Mathematics, vol.\u00a065. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York (1975)"},{"issue":"4","key":"9390_CR2","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1137\/S0036142993258221","volume":"33","author":"M. Ainsworth","year":"1996","unstructured":"Ainsworth, M.: A preconditioner based on domain decomposition for h-p finite-element approximation on quasi-uniform meshes. SIAM J. Numer. Anal. 33(4), 1358\u20131376 (1996)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9390_CR3","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1051\/m2an:2007006","volume":"41","author":"P.F. Antonietti","year":"2007","unstructured":"Antonietti, P.F., Ayuso, B.: Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case. Math. Model. Numer. Anal. 41(1), 21\u201354 (2007)","journal-title":"Math. Model. Numer. Anal."},{"key":"9390_CR4","series-title":"Lect. Notes Comput. Sci. Eng.","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-3-540-75199-1_19","volume-title":"Domain Decomposition Methods in Science and Engineering XVII","author":"P.F. Antonietti","year":"2008","unstructured":"Antonietti, P.F., Ayuso, B.: Class of preconditioners for discontinuous Galerkin approximations of elliptic problems. In: Domain Decomposition Methods in Science and Engineering XVII. Lect. Notes Comput. Sci. Eng., vol. 60, pp. 185\u2013192. Springer, Berlin (2008)"},{"issue":"3","key":"9390_CR5","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1051\/m2an:2008012","volume":"42","author":"P.F. Antonietti","year":"2008","unstructured":"Antonietti, P.F., Ayuso, B.: Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems. M2AN Math. Model. Numer. Anal. 42(3), 443\u2013469 (2008)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"2\u20134","key":"9390_CR6","first-page":"398","volume":"5","author":"P.F. Antonietti","year":"2009","unstructured":"Antonietti, P.F., Ayuso, B.: Two-level Schwarz preconditioners for super penalty discontinuous Galerkin methods. Commun. Comput. Phys. 5(2\u20134), 398\u2013412 (2009)","journal-title":"Commun. Comput. Phys."},{"issue":"4","key":"9390_CR7","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1137\/0719052","volume":"19","author":"D.N. Arnold","year":"1982","unstructured":"Arnold, D.N.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19(4), 742\u2013760 (1982)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"9390_CR8","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D.N. Arnold","year":"2001","unstructured":"Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749\u20131779 (2001\/02) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9390_CR9","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1137\/0728034","volume":"28","author":"I. Babu\u0161ka","year":"1991","unstructured":"Babu\u0161ka, I., Craig, A., Mandel, J., Pitk\u00e4ranta, J.: Efficient preconditioning for the p-version finite element method in two dimensions. SIAM J. Numer. Anal. 28(3), 624\u2013661 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"9390_CR10","first-page":"147","volume-title":"Domain Decomposition Methods","author":"P.E. Bj\u00f8rstad","year":"1989","unstructured":"Bj\u00f8rstad, P.E.: Multiplicative and additive Schwarz methods: convergence in the two-domain case. In: Domain Decomposition Methods, Los Angeles, CA, 1988, pp. 147\u2013159. SIAM, Philadelphia (1989)"},{"issue":"1","key":"9390_CR11","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1137\/S0036142902401311","volume":"41","author":"S.C. Brenner","year":"2003","unstructured":"Brenner, S.C.: Poincar\u00e9-Friedrichs inequalities for piecewise H 1 functions. SIAM J. Numer. Anal. 41(1), 306\u2013324 (2003) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9390_CR12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s00211-005-0641-2","volume":"102","author":"S.C. Brenner","year":"2005","unstructured":"Brenner, S.C., Wang, K.: Two-level additive Schwarz preconditioners for C 0 interior penalty methods. Numer. Math. 102(2), 231\u2013255 (2005)","journal-title":"Numer. Math."},{"key":"9390_CR13","unstructured":"Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.: Discontinuous finite elements for diffusion problems. In: Atti Convegno in onore di F. Brioschi (Milano 1997), pp.\u00a0197\u2013217. Istituto Lombardo, Accademia di Scienze e Lettere (1999)"},{"issue":"4","key":"9390_CR14","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1002\/1098-2426(200007)16:4<365::AID-NUM2>3.0.CO;2-Y","volume":"16","author":"F. Brezzi","year":"2000","unstructured":"Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.: Discontinuous Galerkin approximations for elliptic problems. Numer. Methods Partial Differ. Equ. 16(4), 365\u2013378 (2000)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"1","key":"9390_CR15","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1137\/0913013","volume":"13","author":"X.-C. Cai","year":"1992","unstructured":"Cai, X.-C., Widlund, O.B.: Domain decomposition algorithms for indefinite elliptic problems. SIAM J. Sci. Stat. Comput. 13(1), 243\u2013258 (1992)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"4","key":"9390_CR16","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1137\/0730049","volume":"30","author":"X.-C. Cai","year":"1993","unstructured":"Cai, X.-C., Widlund, O.B.: Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. SIAM J. Numer. Anal. 30(4), 936\u2013952 (1993)","journal-title":"SIAM J. Numer. Anal."},{"key":"9390_CR17","series-title":"Studies in Mathematics and its Applications","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications, vol.\u00a04. North-Holland, Amsterdam (1978)"},{"issue":"6","key":"9390_CR18","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B. Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35(6), 2440\u20132463 (1998) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"23\u201326","key":"9390_CR19","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1016\/j.cma.2003.12.059","volume":"193","author":"C. Dawson","year":"2004","unstructured":"Dawson, C., Sun, S., Wheeler, M.F.: Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Eng. 193(23\u201326), 2565\u20132580 (2004)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"9390_CR20","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1137\/070685841","volume":"46","author":"C.R. Dohrmann","year":"2008","unstructured":"Dohrmann, C.R., Klawonn, A., Widlund, O.B.: Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J. Numer. Anal. 46(4), 2153\u20132168 (2008)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4\u20136","key":"9390_CR21","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.jco.2007.02.003","volume":"23","author":"M. Dryja","year":"2007","unstructured":"Dryja, M., Galvis, J., Sarkis, M.: BDDC methods for discontinuous Galerkin discretization of elliptic problems. J. Complex. 23(4\u20136), 715\u2013739 (2007)","journal-title":"J. Complex."},{"issue":"4","key":"9390_CR22","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF01060030","volume":"6","author":"M. Dubiner","year":"1991","unstructured":"Dubiner, M.: Spectral methods on triangles and other domains. J. Sci. Comput. 6(4), 345\u2013390 (1991)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"9390_CR23","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0720023","volume":"20","author":"S.C. Eisenstat","year":"1983","unstructured":"Eisenstat, S.C., Elman, H.C., Schultz, M.H.: Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20(2), 345\u2013357 (1983)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"9390_CR24","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1137\/S0036142900378480","volume":"39","author":"X. Feng","year":"2001","unstructured":"Feng, X., Karakashian, O.A.: Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal. 39(4), 1343\u20131365 (2001) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2\u20134","key":"9390_CR25","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1504\/IJCSM.2007.016533","volume":"1","author":"E.H. Georgoulis","year":"2007","unstructured":"Georgoulis, E.H., Hall, E., Houston, P.: Discontinuous Galerkin methods on hp-anisotropic meshes. I. A\u00a0priori error analysis. Int. J. Comput. Sci. Math. 1(2\u20134), 221\u2013244 (2007)","journal-title":"Int. J. Comput. Sci. Math."},{"issue":"1","key":"9390_CR26","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1137\/060672352","volume":"30","author":"E.H. Georgoulis","year":"2007\/08","unstructured":"Georgoulis, E.H., Hall, E., Houston, P.: Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. SIAM J. Sci. Comput. 30(1), 246\u2013271 (2007\/08)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"9390_CR27","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s002110200392","volume":"95","author":"J. Gopalakrishnan","year":"2003","unstructured":"Gopalakrishnan, J., Kanschat, G.: A multilevel discontinuous Galerkin method. Numer. Math. 95(3), 527\u2013550 (2003)","journal-title":"Numer. Math."},{"issue":"1","key":"9390_CR28","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s002110050230","volume":"75","author":"B. Guo","year":"1996","unstructured":"Guo, B., Cao, W.: A preconditioner for the h-p version of the finite element method in two dimensions. Numer. Math. 75(1), 59\u201377 (1996)","journal-title":"Numer. Math."},{"issue":"1","key":"9390_CR29","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S0377-0427(97)00063-0","volume":"83","author":"B. Guo","year":"1997","unstructured":"Guo, B., Cao, W.: An iterative and parallel solver based on domain decomposition for the h-p version of the finite element method. J. Comput. Appl. Math. 83(1), 71\u201385 (1997)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"9390_CR30","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1137\/S0036142996299435","volume":"35","author":"B. Guo","year":"1998","unstructured":"Guo, B., Cao, W.: An additive Schwarz method for the h-p version of the finite element method in three dimensions. SIAM J. Numer. Anal. 35(2), 632\u2013654 (1998) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9390_CR31","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00607-002-1446-0","volume":"68","author":"B. Heinrich","year":"2002","unstructured":"Heinrich, B., Pietsch, K.: Nitsche type mortaring for some elliptic problem with corner singularities. Computing 68(3), 217\u2013238 (2002)","journal-title":"Computing"},{"key":"9390_CR32","series-title":"Texts in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-72067-8","volume-title":"Nodal Discontinuous Galerkin Methods","author":"J.S. Hesthaven","year":"2008","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods. Texts in Applied Mathematics, vol.\u00a054. Springer, New York (2008). Algorithms, analysis, and applications"},{"issue":"6","key":"9390_CR33","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1137\/S0036142900374111","volume":"39","author":"P. Houston","year":"2002","unstructured":"Houston, P., Schwab, C., S\u00fcli, E.: Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39(6), 2133\u20132163 (2002) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"243","key":"9390_CR34","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1090\/S0025-5718-03-01484-4","volume":"72","author":"C. Lasser","year":"2003","unstructured":"Lasser, C., Toselli, A.: An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems. Math. Comput. 72(243), 1215\u20131238 (2003) (electronic)","journal-title":"Math. Comput."},{"issue":"4","key":"9390_CR35","first-page":"493","volume":"66","author":"L.F. Pavarino","year":"1994","unstructured":"Pavarino, L.F.: Additive Schwarz methods for the p-version finite element method. Numer. Math. 66(4), 493\u2013515 (1994)","journal-title":"Numer. Math."},{"issue":"2","key":"9390_CR36","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s002110050087","volume":"69","author":"L.F. Pavarino","year":"1994","unstructured":"Pavarino, L.F.: Schwarz methods with local refinement for the p-version finite element method. Numer. Math. 69(2), 185\u2013211 (1994)","journal-title":"Numer. Math."},{"issue":"4","key":"9390_CR37","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1137\/S0036142994265176","volume":"33","author":"L.F. Pavarino","year":"1996","unstructured":"Pavarino, L.F., Widlund, O.B.: A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions. SIAM J. Numer. Anal. 33(4), 1303\u20131335 (1996)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20132","key":"9390_CR38","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0898-1221(96)00230-1","volume":"33","author":"L.F. Pavarino","year":"1997","unstructured":"Pavarino, L.F., Widlund, O.B.: Iterative substructuring methods for spectral elements: problems in three dimensions based on numerical quadrature. Comput. Math. Appl. 33(1\u20132), 193\u2013209 (1997). Approximation theory and applications","journal-title":"Comput. Math. Appl."},{"key":"9390_CR39","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-85268-1","volume-title":"Numerical Approximation of Partial Differential Equations","author":"A. Quarteroni","year":"1994","unstructured":"Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer Series in Computational Mathematics, vol.\u00a023. Springer, Berlin (1994)"},{"key":"9390_CR40","series-title":"Frontiers in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717440","volume-title":"Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations. Theory and Implementation","author":"B. Rivi\u00e8re","year":"2008","unstructured":"Rivi\u00e8re, B.: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations. Theory and Implementation. Frontiers in Applied Mathematics, vol.\u00a035. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2008)"},{"issue":"3\u20134","key":"9390_CR41","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1023\/A:1011546411957","volume":"3","author":"B. Rivi\u00e8re","year":"2000","unstructured":"Rivi\u00e8re, B., Wheeler, M.F., Girault, V.: Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. Comput. Geosci. 3(3\u20134), 337\u2013360 (2000)","journal-title":"Comput. Geosci."},{"issue":"22","key":"9390_CR42","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1002\/nme.1620382204","volume":"38","author":"S.J. Sherwin","year":"1995","unstructured":"Sherwin, S.J., Karniadakis, G.E.: A new triangular and tetrahedral basis for high-order (hp) finite element methods. Int. J. Numer. Methods Eng. 38(22), 3775\u20133802 (1995)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"9390_CR43","volume-title":"Domain Decomposition. Parallel Multilevel Methods for Elliptic Partial Differential Equations","author":"B.F. Smith","year":"1996","unstructured":"Smith, B.F., Bj\u00f8rstad, P.E., Gropp, W.D.: Domain Decomposition. Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, Cambridge (1996)"},{"key":"9390_CR44","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/b137868","volume-title":"Domain Decomposition Methods\u2014Algorithms and Theory","author":"A. Toselli","year":"2005","unstructured":"Toselli, A., Widlund, O.: Domain Decomposition Methods\u2014Algorithms and Theory. Springer Series in Computational Mathematics, vol.\u00a034. Springer, Berlin (2005)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-010-9390-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-010-9390-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-010-9390-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:41:33Z","timestamp":1559464893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-010-9390-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,23]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["9390"],"URL":"https:\/\/doi.org\/10.1007\/s10915-010-9390-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6,23]]}}}