{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T20:02:34Z","timestamp":1777492954025,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,12,17]],"date-time":"2015-12-17T00:00:00Z","timestamp":1450310400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s00211-015-0788-4","type":"journal-article","created":{"date-parts":[[2015,12,17]],"date-time":"2015-12-17T16:56:55Z","timestamp":1450371415000},"page":"741-781","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Superconvergence analysis of Yee scheme for metamaterial Maxwell\u2019s equations on non-uniform rectangular meshes"],"prefix":"10.1007","volume":"134","author":[{"given":"Jichun","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sidney","family":"Shields","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,12,17]]},"reference":[{"key":"788_CR1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10915-007-9144-x","volume":"33","author":"S Adjerid","year":"2007","unstructured":"Adjerid, S., Baccouch, M.: The discontinuous Galerkin method for two-dimensional hyperbolic problems. Part I: superconvergence error analysis. J. Sci. Comput. 33, 75\u2013113 (2007)","journal-title":"J. Sci. Comput."},{"key":"788_CR2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1090\/S0025-5718-1982-0637284-8","volume":"38","author":"DN Arnold","year":"1982","unstructured":"Arnold, D.N., Winther, R.: A superconvergent finite element method for the Korteweg\u2013deVries equation. Math. Comput. 38, 23\u201336 (1982)","journal-title":"Math. Comput."},{"key":"788_CR3","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1137\/S003614290139874X","volume":"41","author":"RE Bank","year":"2004","unstructured":"Bank, R.E., Xu, J.: Asymptotically exact a posteriori error estimators, part I: grids with superconvergence. SIAM J. Numer. Anal. 41, 2294\u20132312 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR4","doi-asserted-by":"crossref","first-page":"2313","DOI":"10.1137\/S0036142901398751","volume":"41","author":"RE Bank","year":"2004","unstructured":"Bank, R.E., Xu, J.: Asymptotically exact a posteriori error estimators, part II: general unstructured grids. SIAM J. Numer. Anal. 41, 2313\u20132332 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR5","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1093\/imanum\/drr001","volume":"32","author":"VA Bokil","year":"2012","unstructured":"Bokil, V.A., Gibson, N.L.: Analysis of spatial high-order finite difference methods for Maxwell\u2019s equations in dispersive media. IMA J. Numer. Anal. 32, 926\u2013956 (2012)","journal-title":"IMA J. Numer. Anal."},{"key":"788_CR6","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.cam.2013.09.031","volume":"265","author":"W Cao","year":"2014","unstructured":"Cao, W.: On the superconvergence patch recovery techniques for the linear finite element approximation on anisotropic meshes. J. Comput. Appl. Math. 265, 33\u201351 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"788_CR7","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s10915-011-9489-z","volume":"50","author":"F Celiker","year":"2012","unstructured":"Celiker, F., Zhang, Z., Zhu, H.: Nodal superconvergence of SDFEM for singularly perturbed problems. J. Sci. Comput. 50, 405\u2013433 (2012)","journal-title":"J. Sci. Comput."},{"key":"788_CR8","volume-title":"High Accuracy Theory of Finite Element Methods (in Chinese)","author":"CM Chen","year":"1995","unstructured":"Chen, C.M., Huang, Y.: High Accuracy Theory of Finite Element Methods (in Chinese). Hunan Science Press, China (1995)"},{"key":"788_CR9","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/s002110050323","volume":"78","author":"H Chen","year":"1998","unstructured":"Chen, H., Ewing, R., Lazarov, R.: Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data. Numer. Math. 78, 495\u2013521 (1998)","journal-title":"Numer. Math."},{"key":"788_CR10","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s00211-007-0123-9","volume":"108","author":"W Chen","year":"2008","unstructured":"Chen, W., Li, X., Liang, D.: Energy-conserved splitting FDTD methods for Maxwells equations. Numer. Math. 108, 445\u2013485 (2008)","journal-title":"Numer. Math."},{"key":"788_CR11","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.jcp.2012.10.019","volume":"235","author":"ET Chung","year":"2013","unstructured":"Chung, E.T., Ciarlet Jr, P., Yu, T.F.: Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwells equations on Cartesian grids. J. Comput. Phys. 235, 14\u201331 (2013)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"788_CR12","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1137\/S0036142901398453","volume":"41","author":"ET Chung","year":"2003","unstructured":"Chung, E.T., Du, Q., Zou, J.: Convergence analysis of a finite volume method for Maxwell\u2019s equations in nonhomogeneous media. SIAM J. Numer. Anal. 41(1), 37\u201363 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR13","volume-title":"Acoustic Metamaterials: Negative Refraction, Imaging, Sensing and Cloaking","year":"2013","unstructured":"Craster, R.V., Guenneau, S. (eds.): Acoustic Metamaterials: Negative Refraction, Imaging, Sensing and Cloaking. Springer, New York (2013)"},{"key":"788_CR14","volume-title":"Electromagnetic Metamaterials: Physics and Engineering Explorations","year":"2006","unstructured":"Engheta, N., Ziolkowski, R.W. (eds.): Electromagnetic Metamaterials: Physics and Engineering Explorations. Wiley, New York (2006)"},{"key":"788_CR15","doi-asserted-by":"crossref","first-page":"2693","DOI":"10.1007\/s11425-011-4305-7","volume":"54","author":"LP Gao","year":"2011","unstructured":"Gao, L.P., Zhang, B.: Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium. Sci. China Math. 54, 2693\u20132712 (2011)","journal-title":"Sci. China Math."},{"key":"788_CR16","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10915-014-9968-0","volume":"65","author":"W Guo","year":"2015","unstructured":"Guo, W., Qiu, J.-M., Qiu, J.: A new LaxWendroff discontinuous Galerkin method with superconvergence. J. Sci. Comput. 65, 299\u2013326 (2015)","journal-title":"J. Sci. Comput."},{"key":"788_CR17","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jcp.2014.03.025","volume":"269","author":"J Hong","year":"2014","unstructured":"Hong, J., Ji, L., Kong, L.: Energy-dissipation splitting finite-difference time-domain method for Maxwell equations with perfectly matched layers. J. Comput. Phys. 269, 201\u2013214 (2014)","journal-title":"J. Comput. Phys."},{"key":"788_CR18","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1002\/num.20703","volume":"28","author":"Y Huang","year":"2012","unstructured":"Huang, Y., Li, J., Lin, Q.: Superconvergence analysis for time-dependent Maxwell\u2019s equations in metamaterials. Numer. Methods Partial Differ. Equ. 28, 1794\u20131816 (2012)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"788_CR19","doi-asserted-by":"crossref","first-page":"B248","DOI":"10.1137\/120869869","volume":"35","author":"Y Huang","year":"2013","unstructured":"Huang, Y., Li, J., Yang, W.: Modeling backward wave propagation in metamaterials by the finite element time-domain method. SIAM J. Sci. Comput. 35, B248\u2013B274 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"788_CR20","doi-asserted-by":"crossref","first-page":"8275","DOI":"10.1016\/j.jcp.2011.07.025","volume":"230","author":"Y Huang","year":"2011","unstructured":"Huang, Y., Li, J., Yang, W., Sun, S.: Superconvergence of mixed finite element approximations to 3-D Maxwells equations in metamaterials. J. Comput. Phys. 230, 8275\u20138289 (2011)","journal-title":"J. Comput. Phys."},{"key":"788_CR21","volume-title":"Finite Element Methods: Superconvergence, Postprocessing and A Posteriori Estimates","year":"1998","unstructured":"Krizek, M., Neittaanam\u00e4ki, P., Stenberg, R. (eds.): Finite Element Methods: Superconvergence, Postprocessing and A Posteriori Estimates. Marcel Dekker, New York (1998)"},{"key":"788_CR22","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.cam.2006.10.031","volume":"209","author":"J Li","year":"2007","unstructured":"Li, J.: Error analysis of mixed finite element methods for wave propagation in double negative metamaterials. J. Comput. Appl. Math. 209, 81\u201396 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"788_CR23","doi-asserted-by":"crossref","first-page":"3161","DOI":"10.1016\/j.cma.2009.05.018","volume":"198","author":"J Li","year":"2009","unstructured":"Li, J.: Numerical convergence and physical fidelity analysis for Maxwells equations in metamaterials. Comput. Methods Appl. Mech. Eng. 198, 3161\u20133172 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"788_CR24","series-title":"Time-domain finite element methods for Maxwell\u2019s equations in metamaterials","volume-title":"Springer Series in Computational Mathematics","author":"J Li","year":"2013","unstructured":"Li, J., Huang, Y.: Springer Series in Computational Mathematics. Time-domain finite element methods for Maxwell\u2019s equations in metamaterials, vol. 43. Springer, New York (2013)"},{"key":"788_CR25","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1137\/S0036142999351212","volume":"38","author":"J Li","year":"2000","unstructured":"Li, J., Wheeler, M.F.: Uniform convergence and superconvergence of mixed finite element methods on anisotropically refined grids. SIAM J. Numer. Anal. 38, 770\u2013798 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR26","first-page":"775","volume":"10","author":"W Li","year":"2013","unstructured":"Li, W., Liang, D., Lin, Y.: A new energy-conserved S-FDTD scheme for Maxwell\u2019s equations in metamaterials. Int. J. Numer. Anal. Model 10, 775\u2013794 (2013)","journal-title":"Int. J. Numer. Anal. Model"},{"key":"788_CR27","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1090\/S0025-5718-07-02039-X","volume":"77","author":"Q Lin","year":"2008","unstructured":"Lin, Q., Li, J.: Superconvergence analysis for Maxwell\u2019s equations in dispersive media. Math. Comput. 77, 757\u2013771 (2008)","journal-title":"Math. Comput."},{"key":"788_CR28","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1090\/S0025-5718-99-01131-X","volume":"69","author":"Q Lin","year":"1999","unstructured":"Lin, Q., Yan, N.: Global superconvergence for Maxwell\u2019s equations. Math. Comput. 69, 159\u2013176 (1999)","journal-title":"Math. Comput."},{"key":"788_CR29","volume-title":"The Construction and Analysis of High Accurate Finite Element Methods (in Chinese)","author":"Q Lin","year":"1996","unstructured":"Lin, Q., Yan, N.: The Construction and Analysis of High Accurate Finite Element Methods (in Chinese). Hebei University Press, Hebei (1996)"},{"key":"788_CR30","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1002\/num.1690100611","volume":"10","author":"P Monk","year":"1994","unstructured":"Monk, P.: Superconvergence of finite element approximations to Maxwells equations. Numer. Methods Partial Differ. Equ. 10, 793\u2013812 (1994)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"788_CR31","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1137\/0731021","volume":"32","author":"P Monk","year":"1994","unstructured":"Monk, P., S\u00fcli, E.: A convergence analysis of Yee\u2019s scheme on nonuniform grids. SIAM J. Numer. Anal. 32, 393\u2013412 (1994)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR32","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1090\/S0025-5718-98-00971-5","volume":"67","author":"RA Nicolaides","year":"1998","unstructured":"Nicolaides, R.A., Wang, D.-Q.: Convergence analysis of a covolume scheme for Maxwell\u2019s equations in three dimensions. Math. Comput. 67, 947\u2013963 (1998)","journal-title":"Math. Comput."},{"key":"788_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-010-9406-x","volume":"46","author":"Z Qiao","year":"2011","unstructured":"Qiao, Z., Yao, C., Jia, S.: Superconvergence and extrapolation analysis of a nonconforming mixed finite element approximation for time-harmonic Maxwell\u2019s equations. J. Sci. Comput. 46, 1\u201319 (2011)","journal-title":"J. Sci. Comput."},{"key":"788_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.amc.2009.01.027","volume":"211","author":"DY Shi","year":"2009","unstructured":"Shi, D.Y., Pei, L.F.: Low order Crouzeix\u2013Raviart type nonconforming finite element methods for the 3D time-dependent Maxwells equations. Appl. Math. Comput. 211, 1\u20139 (2009)","journal-title":"Appl. Math. Comput."},{"key":"788_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0096835","volume-title":"Superconvergence in Galerkin Finite Element Methods","author":"LB Wahlbin","year":"1995","unstructured":"Wahlbin, L.B.: Superconvergence in Galerkin Finite Element Methods. Springer, Berlin (1995)"},{"key":"788_CR36","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1137\/S003614290037589X","volume":"39","author":"J Wang","year":"2001","unstructured":"Wang, J., Ye, X.: Superconvergence of finite element approximations for the Stokes problem by projection methods. SIAM J. Numer. Anal. 39, 1001\u20131013 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"788_CR37","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1364\/OE.11.000662","volume":"11","author":"RW Ziolkowski","year":"2003","unstructured":"Ziolkowski, R.W.: Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs. Opt. Express 11, 662\u2013681 (2003)","journal-title":"Opt. Express"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0788-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-015-0788-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0788-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0788-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T04:47:48Z","timestamp":1718254068000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-015-0788-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,17]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["788"],"URL":"https:\/\/doi.org\/10.1007\/s00211-015-0788-4","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,17]]}}}