{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T17:18:58Z","timestamp":1671729538893},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2013,5]]},"DOI":"10.1007\/s00607-012-0244-6","type":"journal-article","created":{"date-parts":[[2012,11,30]],"date-time":"2012-11-30T04:42:46Z","timestamp":1354250566000},"page":"395-414","source":"Crossref","is-referenced-by-count":3,"title":["An a posteriori error estimator for $$hp$$ -adaptive continuous Galerkin methods for photonic crystal applications"],"prefix":"10.1007","volume":"95","author":[{"given":"Stefano","family":"Giani","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,12,1]]},"reference":[{"key":"244_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032824","volume-title":"A posterior error estimation in finite element analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth M, Oden J (2000) A posterior error estimation in finite element analysis. Wiley, New York"},{"issue":"2\u20134","key":"244_CR2","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/S0045-7825(99)00242-X","volume":"184","author":"P Amestoy","year":"2000","unstructured":"Amestoy P, Duff I, L\u2019Excellent J-Y (2000) Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput Methods Appl Mech Eng 184(2\u20134):501\u2013520","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"6","key":"244_CR3","doi-asserted-by":"crossref","first-page":"2018","DOI":"10.1137\/S0036139902404025","volume":"64","author":"H Ammari","year":"2004","unstructured":"Ammari H, Santosa F (2004) Guided waves in a photonic bandgap structure with a line defect. SIAM J Appl Math 64(6):2018\u20132033","journal-title":"SIAM J Appl Math"},{"key":"244_CR4","volume-title":"Solid state physics","author":"NW Ashcroft","year":"1976","unstructured":"Ashcroft NW, Mermin ND (1976) Solid state physics. Saunders College, Philadelphia"},{"key":"244_CR5","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1006\/jcph.1999.6188","volume":"150","author":"W Axmann","year":"1999","unstructured":"Axmann W, Kuchment P (1999) An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. J Comput Phys 150:468\u2013481","journal-title":"J Comput Phys"},{"key":"244_CR6","doi-asserted-by":"crossref","unstructured":"Babuka I, Osborn, J (1991) Eigenvalue problems. In: Cairlet PG, Lions JL (eds) Handbook of numerical analysis vol II, North Holland, pp 641\u2013787","DOI":"10.1016\/S1570-8659(05)80042-0"},{"issue":"4","key":"244_CR7","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1137\/0725048","volume":"25","author":"I Babu\u0161ka","year":"1988","unstructured":"Babu\u0161ka I, Guo BQ (1988) The h-p version of the finite element method for domains with curved boundaries. SIAM J Numer Anal 25(4):837\u2013861","journal-title":"SIAM J Numer Anal"},{"key":"244_CR8","unstructured":"Birman MS, Suslina TA (1999) A periodic magnetic hamiltonian with a variable metric. The problem of absolute continuity. Petersburg Math J, 10\u201315"},{"key":"244_CR9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00211-006-0037-y","volume":"105","author":"D Boffi","year":"2006","unstructured":"Boffi D, Conforti M, Gastaldi L (2006) Modified edge finite elements for photonic crystals. Numer Math 105:249\u2013266","journal-title":"Numer Math"},{"key":"244_CR10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.physleta.2004.05.030","volume":"327","author":"Y Cao","year":"2004","unstructured":"Cao Y, Hou Z, Liu Y (2004) Convergence problem of plane-wave expansion method for phononic crystals. Phys Lett A 327:247\u2013253","journal-title":"Phys Lett A"},{"key":"244_CR11","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1006\/jcph.1998.6157","volume":"149","author":"DC Dobson","year":"1999","unstructured":"Dobson DC (1999) An efficient method for band structure calculations in 2D photonic crystals. J Comp Phys 149:363\u2013376","journal-title":"J Comp Phys"},{"issue":"2","key":"244_CR12","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1006\/jcph.2000.6521","volume":"161","author":"DC Dobson","year":"2000","unstructured":"Dobson DC, Gopalakrishnan J, Pasciak JE (2000) An efficient method for band structure calculations in 3D photonic crystals. J Comp Phys 161(2):668\u2013679","journal-title":"J Comp Phys"},{"issue":"5","key":"244_CR13","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s00466-006-0107-0","volume":"39","author":"T Eibner","year":"2006","unstructured":"Eibner T, Melenk JM (2006) An adaptive strategy for hp-FEM based on testing for analyticity. Comput Mech 39(5):575\u2013595","journal-title":"Comput Mech"},{"issue":"7","key":"244_CR14","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1002\/nme.2926","volume":"84","author":"C Engstr\u00f6m","year":"2010","unstructured":"Engstr\u00f6m C, Wang M (2010) Complex dispersion relation calculations with the symmetric interior penalty method. Int J Numer Methods Eng 84(7):849\u2013863","journal-title":"Int J Numer Methods Eng"},{"issue":"1","key":"244_CR15","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1103\/PhysRevB.58.180","volume":"58","author":"A Figotin","year":"1998","unstructured":"Figotin A, Gorentsveig V (1998) Localized electromagnetic waves in a layered periodic dielectric medium with a defect. Phys Rev B 58(1):180\u2013188","journal-title":"Phys Rev B"},{"key":"244_CR16","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF02180202","volume":"86","author":"A Figotin","year":"1997","unstructured":"Figotin A, Klein A (1997) Localized classical waves created by defects. J Stat Phys 86:165\u2013177","journal-title":"J Stat Phys"},{"issue":"6","key":"244_CR17","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1137\/S0036139997320536","volume":"58","author":"A Figotin","year":"1998","unstructured":"Figotin A, Klein A (1998) Midgap defect modes in dielectric and acoustic media. SIAM J Appl Math 58(6):1748\u20131773","journal-title":"SIAM J Appl Math"},{"issue":"10","key":"244_CR18","first-page":"2018","volume":"22","author":"S Giani","year":"2012","unstructured":"Giani S (2012) Convergent adaptive finite element methods for photonic crystal applications. Math Mod Meth Appl Sci (M3AS) 22(10):2018\u20132033","journal-title":"Math Mod Meth Appl Sci (M3AS)"},{"issue":"1","key":"244_CR19","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s00211-011-0425-9","volume":"121","author":"S Giani","year":"2011","unstructured":"Giani S, Graham IG (2011) Adaptive finite element methods for conputing band gaps in photonic crystals. Num Math 121(1):31\u201364","journal-title":"Num Math"},{"key":"244_CR20","volume-title":"Photonic crystals: molding the flow of light. 2nd revised edition","author":"J Joannopoulos","year":"2008","unstructured":"Joannopoulos J, Johnson S, Winn J, Meade R (2008) Photonic crystals: molding the flow of light. 2nd revised edition. Princeton University Press, Singapore"},{"key":"244_CR21","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1364\/OE.8.000173","volume":"8","author":"SG Johnson","year":"2001","unstructured":"Johnson SG, Joannopoulos JD (2001) Block-iterative frequency-domain methods for Maxwell\u2019s equations in a planewave basis. Opt Express 8:173\u2013190","journal-title":"Opt Express"},{"key":"244_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8573-7","volume-title":"Floquet theory for partial differential equations","author":"P Kuchment","year":"1993","unstructured":"Kuchment P (1993) Floquet theory for partial differential equations. Birkhauser Verlag, Basel"},{"key":"244_CR23","first-page":"207","volume":"22","author":"P Kuchment","year":"2001","unstructured":"Kuchment P (2001) The mathematics of photonic crystals. SIAM Front Appl Math 22:207\u2013272","journal-title":"SIAM Front Appl Math"},{"key":"244_CR24","doi-asserted-by":"crossref","unstructured":"Lehoucq RB, Sorensen DC, Yang C (1998) ARPACK users\u2019 guide: solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM. ISBN: 0898714079","DOI":"10.1137\/1.9780898719628"},{"key":"244_CR25","doi-asserted-by":"crossref","unstructured":"Luo QHLM, Li Z (2009) Spectral element method for band structures of two-dimensional anisotropic photonic crystals. Phys Rev E 79:026705","DOI":"10.1103\/PhysRevE.79.026705"},{"issue":"1\u20132","key":"244_CR26","first-page":"367391","volume":"171","author":"M Marletta","year":"2004","unstructured":"Marletta M (2004) Eigenvalue problems on exterior domains and Dirichlet to Neumann maps. J Comput Appl Math 171(1\u20132):367391","journal-title":"J Comput Appl Math"},{"issue":"8","key":"244_CR27","doi-asserted-by":"crossref","first-page":"4809","DOI":"10.1103\/PhysRevB.58.4809","volume":"58","author":"A Mekis","year":"1998","unstructured":"Mekis A, Fan S, Joannopoulos JD (1998) Bound states in photonic crystal waveguides and waveguide bends. Phys Rev B 58(8):4809\u20134817","journal-title":"Phys Rev B"},{"issue":"1","key":"244_CR28","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1023\/A:1014268310921","volume":"15","author":"J Melenk","year":"2001","unstructured":"Melenk J, Wohlmuth B (2001) On residual-based a posteriori error estimation in hp-FEM. Adv Comput Math 15(1):311\u2013331","journal-title":"Adv Comput Math"},{"issue":"1","key":"244_CR29","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1137\/S0036142903432930","volume":"43","author":"JM Melenk","year":"2005","unstructured":"Melenk JM (2005) hp-interpolation of nonsmooth functions and an application to hp-a posteriori error estimation. SIAM J Numer Anal 43(1):127","journal-title":"SIAM J Numer Anal"},{"issue":"6","key":"244_CR30","doi-asserted-by":"crossref","first-page":"4356","DOI":"10.1137\/090756545","volume":"47","author":"R Norton","year":"2010","unstructured":"Norton R, Scheichl R (2010) Convergence analysis of planewave expansion methods for 2D Schr\u00f6dinger operators with discontinuous periodic potentials. SIAM J Numer Anal 47(6):4356\u20134380","journal-title":"SIAM J Numer Anal"},{"key":"244_CR31","doi-asserted-by":"crossref","unstructured":"Norton RA, Scheichl R (2013) Planewave expansion methods for photonic crystal fibres. Appl Numer Math 63:88\u2013104","DOI":"10.1016\/j.apnum.2012.09.008"},{"issue":"19","key":"244_CR32","doi-asserted-by":"crossref","first-page":"195108","DOI":"10.1103\/PhysRevB.71.195108","volume":"71","author":"GJ Pearce","year":"2005","unstructured":"Pearce GJ, Hedley TD, Bird DM (2005) Adaptive curvilinear coordinates in a plane-wave solution of Maxwell\u2019s equations in photonic crystals. Phys Rev B 71(19):195108","journal-title":"Phys Rev B"},{"key":"244_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-14324-7","volume-title":"Optical properties of photonic crystals","author":"K Sakoda","year":"2001","unstructured":"Sakoda K (2001) Optical properties of photonic crystals. Springer, Berlin"},{"issue":"7","key":"244_CR34","doi-asserted-by":"crossref","first-page":"7307","DOI":"10.1364\/OE.18.007307","volume":"18","author":"K Schmidt","year":"2010","unstructured":"Schmidt K, Kappeler R (2010) Efficient computation of photonic crystal waveguide modes with dispersive material. Opt Express 18(7):7307\u20137322","journal-title":"Opt Express"},{"key":"244_CR35","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1016\/j.cma.2008.06.009","volume":"198","author":"K Schmidt","year":"2009","unstructured":"Schmidt K, Kauf P (2009) Computation of the band structure of two-dimensional photonic crystals with hp finite elements. Comput Methods Appl Mech Eng 198:1249\u20131259","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"244_CR36","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1137\/040616875","volume":"43","author":"S Soussi","year":"2005","unstructured":"Soussi S (2005) Convergence of the supercell method for defect modes calculations in photonic crystals. SIAM J Numer Anal 43(3):1175\u20131201","journal-title":"SIAM J Numer Anal"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-012-0244-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00607-012-0244-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-012-0244-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,6]],"date-time":"2019-07-06T07:57:07Z","timestamp":1562399827000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00607-012-0244-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,1]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["244"],"URL":"https:\/\/doi.org\/10.1007\/s00607-012-0244-6","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,1]]}}}