{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T07:00:14Z","timestamp":1756191614401},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2006,7,1]],"date-time":"2006-07-01T00:00:00Z","timestamp":1151712000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2006,7]]},"DOI":"10.1007\/s10444-004-7619-y","type":"journal-article","created":{"date-parts":[[2006,6,27]],"date-time":"2006-06-27T13:29:35Z","timestamp":1151414975000},"page":"259-286","source":"Crossref","is-referenced-by-count":9,"title":["An analysis of discontinuous Galerkin methods for elliptic problems"],"prefix":"10.1007","volume":"25","author":[{"given":"Reinhold","family":"Schneider","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuesheng","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aihui","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"7619_CR1","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"1975","unstructured":"R.A. Adams, Sobolev Spaces (Academic Press, New York, 1975)."},{"key":"7619_CR2","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1137\/0719052","volume":"19","author":"D.N. Arnold","year":"1982","unstructured":"D.N. Arnold, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal. 19 (1982) 742\u2013760.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR3","series-title":"Lectures in Computational Science and Engineering","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/978-3-642-59721-3_5","volume-title":"Discontinuous Galerkin Methods","author":"D.N. Arnold","year":"2000","unstructured":"D.N. Arnold, F. Brezzi, B. Cockburn and D. Marini, Discontinuous Galerkin methods for elliptic problems, in: Discontinuous Galerkin Methods, eds. B. Cockburn, G.E. Karniadakis and C.-W. Shu, Lectures in Computational Science and Engineering, Vol. 11 (Springer, Berlin, 2000) pp. 89\u2013101."},{"key":"7619_CR4","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D.N. Arnold","year":"2001\/2002","unstructured":"D.N. Arnold, F. Brezzi, B. Cockburn and D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal. 39 (2001\/2002) 1749\u20131779.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR5","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1090\/S0025-5718-1973-0351118-5","volume":"27","author":"I. Babuska","year":"1973","unstructured":"I. Babuska, The finite element method with penalty, Math. Comp. 27 (1973) 221\u2013228.","journal-title":"Math. Comp."},{"key":"7619_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(87)90114-9","volume":"61","author":"I. Babuska","year":"1987","unstructured":"I. Babuska and A.D. Miller, A feedback finite element method with a posteriori error estimation, Part 1, Comput. Methods Appl. Mech. Engrg. 61 (1987) 1\u201340.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7619_CR7","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1137\/0715049","volume":"15","author":"I. Babuska","year":"1978","unstructured":"I. Babuska and C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736\u2013754.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR8","volume-title":"Accuracy Estimates and Adaptive Refinements in Finite Element Computations","author":"I. Babuska","year":"1986","unstructured":"I. Babuska, O.C. Zienkiewicz, J. Gago and E.R. de A. Oliveira, Accuracy Estimates and Adaptive Refinements in Finite Element Computations (Wiley, New York, 1986)."},{"key":"7619_CR9","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1137\/0710071","volume":"10","author":"I. Babuska","year":"1973","unstructured":"I. Babuska and M. Zlamal, Nonconforming elements in the finite element method with penalty, SIAM J. Numer. Anal. 10 (1973) 863\u2013875.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900002610","volume":"5","author":"R.E. Bank","year":"1996","unstructured":"R.E. Bank, Hierarchical bases and the finite element method, Acta Numerica 5 (1996) 1\u201343.","journal-title":"Acta Numerica"},{"key":"7619_CR11","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1137\/S1064827599353701","volume":"22","author":"R.E. Bank","year":"2001","unstructured":"R.E. Bank and M. Holst, A new paradigm for parallel adaptive meshing algorithms, SIAM J. Sci. Comput. 22 (2001) 1411\u20131443.","journal-title":"SIAM J. Sci. Comput."},{"key":"7619_CR12","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1006\/jcph.1996.5572","volume":"131","author":"F. Bassi","year":"1997","unstructured":"F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier\u2013Stokes equations, J. Comput. Phys. 131 (1997) 267\u2013279.","journal-title":"J. Comput. Phys."},{"key":"7619_CR13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0045-7825(98)00359-4","volume":"175","author":"C.E. Baumann","year":"1999","unstructured":"C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection\u2013diffusion problems, Comput. Methods Appl. Mech. Engrg. 175 (1999) 311\u2013341.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7619_CR14","unstructured":"R. Becker and P. Hansbo, A finite element method for domain decomposition with non-matching grids, Report No. 3616, RINRIA (1999)."},{"key":"7619_CR15","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1137\/S0036142995293766","volume":"35","author":"C. Bernardi","year":"1998","unstructured":"C. Bernardi and V. Girault, A local regularization operator for triangular and quadrilateral finite elements, SIAM J. Numer. Anal. 35 (1998) 1893\u20131916.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR16","doi-asserted-by":"crossref","first-page":"3391","DOI":"10.1016\/S0045-7825(02)00254-2","volume":"191","author":"C.L. Bottasso","year":"2002","unstructured":"C.L. Bottasso, S. Micheletti and R. Sacco, The discontinuous Petrov\u2013Galerkin method for elliptic problems, Comput. Methods Appl. Mech. Engrg. 191 (2002) 3391\u20133409.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7619_CR17","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":"F. Brezzi, G. Manzini, D. Marini, P. Pietra and A. Russo, Discontinuous Galerkin approximations for elliptic problems, Numer. Methods Partial Differential Equations 16 (2000) 365\u2013378.","journal-title":"Numer. Methods Partial Differential Equations"},{"key":"7619_CR18","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1137\/S003614299732334X","volume":"36","author":"C. Carstensen","year":"1999","unstructured":"C. Carstensen and R. Verf\u00fcrth, Edge residuals dominate a posteriori error estimates for linear finite element methods, SIAM J. Numer. Anal. 36 (1999) 1571\u20131587.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR19","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1137\/S0036142900371003","volume":"38","author":"P. Castillo","year":"2000","unstructured":"P. Castillo, B. Cockburn, I. Perugia and D. Sch\u00f6tzau, An a priori error analysis of the local discontinuous Galerkin method for elliptic problems, SIAM J. Numer. Anal. 38 (2000) 1676\u20131706.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR20","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1090\/S0025-5718-01-01317-5","volume":"71","author":"P. Castillo","year":"2002","unstructured":"P. Castillo, B. Cockburn, D. Sch\u00f6tzau and C. Schwab, Optimal a priori error estimates for thehp-version of the local discontinuous Galerkin method for convection\u2013diffusion problems, Math. Comp. 71 (2002), 455\u2013478.","journal-title":"Math. Comp."},{"key":"7619_CR21","volume-title":"Handbook of Numerical Analysis","author":"P.G. Ciarlet","year":"1991","unstructured":"P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part I) (North-Holland, Amsterdam, 1991)."},{"key":"7619_CR22","first-page":"77","volume":"9","author":"P. Cl\u00e9ment","year":"1975","unstructured":"P. Cl\u00e9ment, Approximation by finite element functions using local regularization, RAIRO Anal. Numer. 9 (1975) 77\u201384.","journal-title":"RAIRO Anal. Numer."},{"key":"7619_CR23","series-title":"Lectures in Computational Science and Engineering","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59721-3","volume-title":"Discontinuous Galerkin Methods","author":"B. Cockburn","year":"2000","unstructured":"B. Cockburn, G.E. Karniadakis and C.-W. Shu, Discontinuous Galerkin Methods, Lectures in Computational Science and Engineering, Vol. 11 (Springer, Berlin, 2000)."},{"key":"7619_CR24","series-title":"Lectures in Computational Science and Engineering","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-59721-3","volume-title":"Discontinuous Galerkin Methods","author":"B. Cockburn","year":"2000","unstructured":"B. Cockburn, G.E. Karniadakis and C.-W. Shu, The development of discontinuous Galerkin methods, in: Discontinuous Galerkin Methods, eds. B. Cockburn, G.E. Karniadakis and C.-W. Shu, Lectures in Computational Science and Engineering, Vol. 11 (Springer, Berlin, 2000) pp. 1\u201350."},{"key":"7619_CR25","doi-asserted-by":"crossref","unstructured":"J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, in: Lecture Notes in Physics, Vol. 58 (1976) pp. 207\u2013216.","DOI":"10.1007\/BFb0120591"},{"key":"7619_CR26","doi-asserted-by":"crossref","unstructured":"K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations, Acta Numerica (1995) 105\u2013158.","DOI":"10.1017\/S0962492900002531"},{"key":"7619_CR27","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/S0252-9602(18)30264-9","volume":"11","author":"Q. Lin","year":"1991","unstructured":"Q. Lin and A. Zhou, Some arguments for recovering the finite element error of hyperbolic problems, Acta Math. Sci. 11 (1991) 471\u2013476.","journal-title":"Acta Math. Sci."},{"key":"7619_CR28","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02995904","volume":"36","author":"J.A. Nitsche","year":"1971","unstructured":"J.A. Nitsche, \u00dcber ein Variationsprinzip zur L\u00f6sung Dirichlet-Problemen bei Verwendung von Teilr\u00e4umen, die keinen Randbedingungen unteworfen sind, Abh. Math. Sem. Univ. Hamburg 36 (1971) 9\u201315.","journal-title":"Abh. Math. Sem. Univ. Hamburg"},{"key":"7619_CR29","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1090\/S0025-5718-1974-0373325-9","volume":"28","author":"J.A. Nitsche","year":"1974","unstructured":"J.A. Nitsche and A.H. Schatz, Interiori estimates for Ritz\u2013Galerkin methods, Math. Comp. 28 (1974) 937\u2013955.","journal-title":"Math. Comp."},{"key":"7619_CR30","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1006\/jcph.1998.6032","volume":"146","author":"J.T. Oden","year":"1998","unstructured":"J.T. Oden, I. Babuska and C.E. Baumann, A discontinuous hp finite element method for diffusion problems, J. Comput. Phys. 146 (1998) 491\u2013519.","journal-title":"J. Comput. Phys."},{"key":"7619_CR31","series-title":"Lectures in Computational Science and Engineering","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/978-3-642-59721-3_17","volume-title":"Discontinuous Galerkin Methods","author":"B. Riviere","year":"2000","unstructured":"B. Riviere and F. Wheeler, A discontinuous Galerkin method applied to nonlinear parabolic equations, in: Discontinuous Galerkin Methods, eds. B. Cockburn, G.E. Karniadakis and C.-W. Shu, Lectures in Computational Science and Engineering, Vol. 11 (Springer, Berlin, 2000) pp. 231\u2013244."},{"key":"7619_CR32","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1137\/S003614290037174X","volume":"39","author":"B. Riviere","year":"2001","unstructured":"B. Riviere, M.F. Wheeler and V. Girault, A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems, SIAM J. Numer. Anal. 39 (2001) 902\u2013931.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR33","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1090\/S0025-5718-1977-0431753-X","volume":"31","author":"A.H. Schatz","year":"1977","unstructured":"A.H. Schatz and L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, Math. Comp. 31 (1977) 414\u2013442.","journal-title":"Math. Comp."},{"key":"7619_CR34","first-page":"907","volume":"64","author":"A.H. Schatz","year":"1995","unstructured":"A.H. Schatz and L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, Part II, Math. Comp. 64 (1995) 907\u2013928.","journal-title":"Math. Comp."},{"key":"7619_CR35","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"L.R. Scott","year":"1992","unstructured":"L.R. Scott and S. Zhang, Finite element interpolation of mpon-smooth functions satisfying boundary conditions, Math. Comp. 54 (1992) 483\u2013493.","journal-title":"Math. Comp"},{"key":"7619_CR36","series-title":"Lectures in Computational Science and Engineering","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/978-3-642-59721-3_16","volume-title":"Discontinuous Galerkin Methods","author":"E. S\u00fcli","year":"2000","unstructured":"E. S\u00fcli, C. Schwab and P. Houston, hp-DGFEM for partial differential equations with nonnegative characteristic form, in: Discontinuous Galerkin Methods, eds. B. Cockburn, G.E. Karniadakis and C.-W. Shu, Lectures in Computational Science and Engineering, Vol. 11 (Springer, Berlin, 2000) pp. 221\u2013230."},{"key":"7619_CR37","doi-asserted-by":"crossref","first-page":"445","DOI":"10.2307\/2153518","volume":"62","author":"R. Verf\u00fcrth","year":"1994","unstructured":"R. Verf\u00fcrth, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comp. 62 (1994) 445\u2013475.","journal-title":"Math. Comp."},{"key":"7619_CR38","doi-asserted-by":"crossref","unstructured":"R. Verf\u00fcrth, A posteriori error estimates for nonlinear problems. Finite element discretizations of parabolic equations, Bericht Nr. 180, Fakult\u00e4t f\u00fcr Mathematik, Ruhr-Universit\u00e4t Bochum (1995).","DOI":"10.2307\/2153518"},{"key":"7619_CR39","unstructured":"R. Verf\u00fcrth, A Review of A-Posteriori Error Estimation and Adaptive Mesh Refinement (Wiley\/Teubner, 1996)."},{"key":"7619_CR40","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s002110050381","volume":"80","author":"R. Verf\u00fcrth","year":"1998","unstructured":"R. Verf\u00fcrth, A posteriori error estimators for convection-diffusion equations, Numer. Math. 80 (1998) 641\u2013663.","journal-title":"Numer. Math."},{"key":"7619_CR41","doi-asserted-by":"crossref","unstructured":"L.B. Wahlbin, Local behavior in finite element methods, in [17] (1991) 355\u2013522.","DOI":"10.1016\/S1570-8659(05)80040-7"},{"key":"7619_CR42","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1137\/0715010","volume":"15","author":"M.F. Wheeler","year":"1978","unstructured":"M.F. Wheeler, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal. 15 (1978) 152\u2013161.","journal-title":"SIAM J. Numer. Anal."},{"key":"7619_CR43","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s002110050467","volume":"84","author":"B.I. Wohlmuth","year":"1999","unstructured":"B.I. Wohlmuth, A residual based error estimator for mortar finite element discretizations, Numer. Math. 84 (1999) 143\u2013171.","journal-title":"Numer. Math."},{"key":"7619_CR44","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1090\/S0025-5718-99-01149-7","volume":"69","author":"J. Xu","year":"2000","unstructured":"J. Xu and A. Zhou, Local and parallel finite element algorithms based on two-grid discretizations, Math. Comp. 69 (2000) 881\u2013909.","journal-title":"Math. Comp."},{"key":"7619_CR45","unstructured":"J. Xu and A. Zhou, Locality and parallelization of finite elements, in: Proc. of the 11th Domain Decomposition Methods, eds. C.H. Lai, P.E. Bj\u00f8rstad, M. Cross and O.B. Widlund, DDM.org (1999) pp. 140\u2013147."},{"key":"7619_CR46","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1023\/A:1014284306804","volume":"15","author":"N. Yan","year":"2001","unstructured":"N. Yan, A posteriori error estimators of gradient recovery type for elliptic obstacle problems, Adv. Comput. Math. 15 (2001) 333\u2013362.","journal-title":"Adv. Comput. Math."},{"key":"7619_CR47","doi-asserted-by":"crossref","first-page":"4289","DOI":"10.1016\/S0045-7825(00)00319-4","volume":"190","author":"N. Yan","year":"2001","unstructured":"N. Yan and A. Zhou, Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes, Comput. Methods Appl. Mech. Engrg. 190 (2001) 4289\u20134399.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7619_CR48","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S0045-7825(97)00260-0","volume":"158","author":"A. Zhou","year":"1998","unstructured":"A. Zhou, C.L. Liem, T.M. Shih and T. L\u00fc, Error analysis on bi-parameter finite elements, Comput. Methods Appl. Mech. Engrg. 158 (1998) 329\u2013339.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7619_CR49","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1002\/nme.1620330702","volume":"33","author":"O.C. Zienkiewicz","year":"1992","unstructured":"O.C. Zienkiewicz and J.Z. Zhu, The supercovergent patch recovery and a posteriori error estimates, Internat. J. Numer. Methods Engrg. 33 (1992) 1331\u20131382.","journal-title":"Internat. J. Numer. Methods Engrg."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-004-7619-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-004-7619-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-004-7619-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:08Z","timestamp":1559149688000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-004-7619-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":49,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["7619"],"URL":"https:\/\/doi.org\/10.1007\/s10444-004-7619-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7]]}}}