{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T16:12:15Z","timestamp":1772986335798,"version":"3.50.1"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T00:00:00Z","timestamp":1535500800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Scientific Independence of Young Researchers","award":["RBSI14VT0S"],"award-info":[{"award-number":["RBSI14VT0S"]}]},{"name":"GNCS-INdAM"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s10915-018-0802-y","type":"journal-article","created":{"date-parts":[[2018,8,30]],"date-time":"2018-08-30T03:00:02Z","timestamp":1535598002000},"page":"1339-1370","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods"],"prefix":"10.1007","volume":"77","author":[{"given":"Paola F.","family":"Antonietti","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3588-2029","authenticated-orcid":false,"given":"Paul","family":"Houston","sequence":"additional","affiliation":[]},{"given":"Giorgio","family":"Pennesi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,8,29]]},"reference":[{"issue":"21\u201326","key":"802_CR1","doi-asserted-by":"publisher","first-page":"1651","DOI":"10.1016\/j.cma.2008.12.033","volume":"198","author":"PF Antonietti","year":"2009","unstructured":"Antonietti, P.F., Brezzi, F., Marini, L.D.: Bubble stabilization of discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 198(21\u201326), 1651\u20131659 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"802_CR2","doi-asserted-by":"crossref","unstructured":"Antonietti, P.F., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E.H., Giani, S., Houston, P.: Review of discontinuous Galerkin Finite Element Methods for partial differential equations on complicated domains, Lecture Notes in Computational Science and Engineering, vol. 114, 1st edn., chap.\u00a08, pp. 281\u2013310. Springer (2016)","DOI":"10.1007\/978-3-319-41640-3_9"},{"key":"802_CR3","unstructured":"Antonietti, P.F., Facciol\u00e0, C., Russo, A., Verani, M.: Discontinuous Galerkin approximation of flows in fractured porous media. Technical Report 22\/2016, MOX Report (2016)"},{"issue":"3","key":"802_CR4","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1051\/m2an\/2015087","volume":"50","author":"PF Antonietti","year":"2016","unstructured":"Antonietti, P.F., Formaggia, L., Scotti, A., Verani, M., Verzott, N.: Mimetic Finite Difference approximation of flows in fractured porous media. ESAIM Math. Model. Numer. Anal. 50(3), 809\u2013832 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"3","key":"802_CR5","doi-asserted-by":"publisher","first-page":"A1417","DOI":"10.1137\/120877246","volume":"35","author":"PF Antonietti","year":"2013","unstructured":"Antonietti, P.F., Giani, S., Houston, P.: $$hp$$ hp -version Composite Discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM J. Sci. Comput. 35(3), A1417\u2013A1439 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"802_CR6","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10915-013-9792-y","volume":"60","author":"PF Antonietti","year":"2014","unstructured":"Antonietti, P.F., Giani, S., Houston, P.: Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. J. Sci. Comput. 60(1), 203\u2013227 (2014)","journal-title":"J. Sci. Comput."},{"key":"802_CR7","doi-asserted-by":"crossref","unstructured":"Antonietti, P.F., Houston, P., Pennesi, G.: Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods. MOX Report No. 03\/2018 (2018)","DOI":"10.1007\/s10915-018-0802-y"},{"key":"802_CR8","doi-asserted-by":"crossref","unstructured":"Antonietti, P.F., Manzini, G., Verani, M.: The fully nonconforming Virtual Element Method for biharmonic problems. Math. Mod. Methods Appl. Sci. (Accepted: 16 October 2017)","DOI":"10.1142\/S0218202518500100"},{"key":"802_CR9","unstructured":"Antonietti, P.F., Pennesi, G.: V-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes. MOX Report No. 49\/2017 (submitted 2017)"},{"issue":"1","key":"802_CR10","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1137\/13091141X","volume":"52","author":"PF Antonietti","year":"2014","unstructured":"Antonietti, P.F., da Veiga, L.B., Mora, D., Verani, M.: A stream Virtual Element formulation of the Stokes problem on polygonal meshes. SIAM J. Numer. Anal. 52(1), 386\u2013404 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"802_CR11","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1137\/15M1008117","volume":"54","author":"PF Antonietti","year":"2016","unstructured":"Antonietti, P.F., da Veiga, L.B., Scacchi, S., Verani, M.: A C1 Virtual Element Method for the Cahn\u2013Hilliard equation with polygonal meshes. SIAM J. Numer. Anal. 54(1), 34\u201356 (2016)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"802_CR12","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"Douglas N. Arnold","year":"2002","unstructured":"Arnold, N.D., 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\/2002)","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"3","key":"802_CR13","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1051\/m2an\/2015090","volume":"50","author":"B Ayuso de Dios","year":"2016","unstructured":"Ayuso de Dios, B., Lipnikov, K., Manzini, G.: The nonconforming Virtual Element Method. ESAIM Math. Model. Numer. Anal. 50(3), 879\u2013904 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"8","key":"802_CR14","doi-asserted-by":"publisher","first-page":"1495","DOI":"10.1142\/S0218202514400028","volume":"24","author":"F Bassi","year":"2014","unstructured":"Bassi, F., Botti, L., Colombo, A.: Agglomeration-based physical frame dG discretizations: an attempt to be mesh free. Math. Mod. Methods Appl. Sci. 24(8), 1495\u20131539 (2014)","journal-title":"Math. Mod. Methods Appl. Sci."},{"issue":"1","key":"802_CR15","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1142\/S0218202512500492","volume":"23","author":"L Beir\u00e3o da Veiga","year":"2013","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of Virtual Element Methods. Math. Models Methods Appl. Sci. 23(1), 199\u2013214 (2013)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"802_CR16","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1051\/m2an\/2015067","volume":"50","author":"L Beir\u00e3o da Veiga","year":"2016","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes. ESAIM Math. Model. Numer. Anal. 50(3), 727\u2013747 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"4","key":"802_CR17","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1142\/S0218202516500160","volume":"26","author":"L Beir\u00e3o da Veiga","year":"2016","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: Virtual Element Method for general second-order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26(4), 729\u2013750 (2016)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"802_CR18","volume-title":"The Mimetic Finite Difference Method for Elliptic Problems","author":"L Beir\u00e3o da Veiga","year":"2014","unstructured":"Beir\u00e3o da Veiga, L., Lipnikov, K., Manzini, G.: The Mimetic Finite Difference Method for Elliptic Problems, vol. 11. Springer, Cham (2014)"},{"issue":"5","key":"802_CR19","doi-asserted-by":"publisher","first-page":"1872","DOI":"10.1137\/040613950","volume":"43","author":"Franco Brezzi","year":"2005","unstructured":"Brezzi, F., Lipnikov, K., Shashkov, M.: Convergence of the Mimetic Finite Difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal. 43(5), 1872\u20131896 (electronic) (2005)","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"2","key":"802_CR20","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1142\/S0218202506001157","volume":"16","author":"F Brezzi","year":"2006","unstructured":"Brezzi, F., Lipnikov, K., Shashkov, M.: Convergence of Mimetic Finite Difference method for diffusion problems on polyhedral meshes with curved faces. Math. Mod. Methods Appl. Sci. 16(2), 275\u2013297 (2006)","journal-title":"Math. Mod. Methods Appl. Sci."},{"issue":"10","key":"802_CR21","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1142\/S0218202505000832","volume":"15","author":"F Brezzi","year":"2005","unstructured":"Brezzi, F., Lipnikov, K., Simoncini, V.: A family of Mimetic Finite Difference methods on polygonal and polyhedral meshes. Math. Mod. Methods Appl. S. 15(10), 1533\u20131551 (2005)","journal-title":"Math. Mod. Methods Appl. S."},{"issue":"4","key":"802_CR22","doi-asserted-by":"publisher","first-page":"A1251","DOI":"10.1137\/16M1073285","volume":"39","author":"A Cangiani","year":"2017","unstructured":"Cangiani, A., Dong, Z., Georgoulis, E.H.: $$hp$$ hp -Version space\u2013time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM J. Sci. Comput. 39(4), A1251\u2013A1279 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"802_CR23","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1051\/m2an\/2015059","volume":"50","author":"A Cangiani","year":"2016","unstructured":"Cangiani, A., Dong, Z., Georgoulis, E.H., Houston, P.: $$hp$$ hp -Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM Math. Model. Numer. Anal. 50, 699\u2013725 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"802_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-67673-9","volume-title":"$$hp$$ hp","author":"A Cangiani","year":"2017","unstructured":"Cangiani, A., Dong, Z., Georgoulis, E.H., Houston, P.: $$hp$$ hp -Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Springer International Publishing, SpringerBriefs in Mathematics, Berlin (2017)"},{"issue":"10","key":"802_CR25","doi-asserted-by":"publisher","first-page":"2009","DOI":"10.1142\/S0218202514500146","volume":"24","author":"A Cangiani","year":"2014","unstructured":"Cangiani, A., Georgoulis, E.H., Houston, P.: $$hp$$ hp -Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. 24(10), 2009\u20132041 (2014)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"802_CR26","first-page":"1317","volume":"37","author":"A Cangiani","year":"2017","unstructured":"Cangiani, A., Manzini, G., Sutton, O.J.: Conforming and nonconforming Virtual Element Methods for elliptic problems. IMA J. Numer. Anal. 37(3), 1317\u20131354 (2017)","journal-title":"IMA J. Numer. Anal."},{"issue":"6","key":"802_CR27","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1007\/s00466-015-1213-7","volume":"56","author":"EB Chin","year":"2015","unstructured":"Chin, E.B., Lasserre, J.B., Sukumar, N.: Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra. Comput. Mech. 56(6), 967\u2013981 (2015)","journal-title":"Comput. Mech."},{"issue":"11","key":"802_CR28","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1002\/nme.5436","volume":"110","author":"EB Chin","year":"2017","unstructured":"Chin, E.B., Lasserre, J.B., Sukumar, N.: Modeling crack discontinuities without element-partitioning in the extended finite element method. Int. J. Numer. Methods Eng. 110(11), 1021\u20131048 (2017)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"264","key":"802_CR29","doi-asserted-by":"publisher","first-page":"1887","DOI":"10.1090\/S0025-5718-08-02123-6","volume":"77","author":"B Cockburn","year":"2008","unstructured":"Cockburn, B., Dond, B., Guzm\u00e1n, J.: A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Math. Comput. 77(264), 1887\u20131916 (2008)","journal-title":"Math. Comput."},{"issue":"2","key":"802_CR30","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","volume":"47","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Gopalakrishnan, J., Lazarov, R.: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319\u20131365 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"271","key":"802_CR31","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1090\/S0025-5718-10-02334-3","volume":"79","author":"B Cockburn","year":"2010","unstructured":"Cockburn, B., Gopalakrishnan, J., Sayas, F.J.: A projection-based error analysis of HDG methods. Math. Comput. 79(271), 1351\u20131367 (2010)","journal-title":"Math. Comput."},{"issue":"265","key":"802_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0025-5718-08-02146-7","volume":"78","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Guzm\u00e1n, J., Wang, H.: Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Math. Comput. 78(265), 1\u201324 (2009)","journal-title":"Math. Comput."},{"issue":"1","key":"802_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2014.09.009","volume":"283","author":"DA Di Pietro","year":"2015","unstructured":"Di Pietro, D.A., Ern, A.: A hybrid high-order locking-free method for linear elasticity on general meshes. Comput. Methods Appl. Mech. Eng. 283(1), 1\u201321 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"802_CR34","first-page":"31","volume":"353","author":"DA Di Pietro","year":"2015","unstructured":"Di Pietro, D.A., Ern, A.: Hybrid High-Order methods for variable-diffusion problems on general meshes. C. R. Math. Acad. Sci. Soc. R. Can. 353(1), 31\u201334 (2015)","journal-title":"C. R. Math. Acad. Sci. Soc. R. Can."},{"issue":"4","key":"802_CR35","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1515\/cmam-2014-0018","volume":"14","author":"DA Di Pietro","year":"2014","unstructured":"Di Pietro, D.A., Ern, A., Lemaire, S.: An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput. Method Appl. Math. 14(4), 461\u2013472 (2014)","journal-title":"Comput. Method Appl. Math."},{"issue":"3","key":"802_CR36","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1051\/m2an\/2015079","volume":"50","author":"J Droniou","year":"2016","unstructured":"Droniou, J., Eymard, R., Herbin, R.: Gradient schemes: generic tools for the numerical analysis of diffusion equations. ESAIM Math. Model. Numer. Anal. 50(3), 749\u2013781 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"3","key":"802_CR37","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/nme.2914","volume":"84","author":"TP Fries","year":"2010","unstructured":"Fries, T.P., Belytschko, T.: The extended\/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Methods Eng. 84(3), 253\u2013304 (2010)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"19\u201320","key":"802_CR38","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1016\/j.cma.2007.07.002","volume":"197","author":"A Gerstenberger","year":"2008","unstructured":"Gerstenberger, A., Wall, A.W.: An Extended Finite Element Method\/Lagrange multiplier based approach for fluid-structure interaction. Comput. Methods Appl. Mech. Eng. 197(19\u201320), 1699\u20131714 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"802_CR39","doi-asserted-by":"crossref","first-page":"123","DOI":"10.4208\/nmtma.2014.1311nm","volume":"7","author":"S Giani","year":"2014","unstructured":"Giani, S., Houston, P.: Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows. Numer. Math. Theory Methods Appl. 7(2), 123\u2013148 (2014)","journal-title":"Numer. Math. Theory Methods Appl."},{"key":"802_CR40","volume-title":"Introduction to Quantum Mechanics","author":"DJ Griffiths","year":"2005","unstructured":"Griffiths, D.J.: Introduction to Quantum Mechanics. Pearson Education, London (2005)"},{"issue":"1","key":"802_CR41","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/s007910050002","volume":"1","author":"W. Hackbusch","year":"1997","unstructured":"Hackbusch, W., Sauter, S.A.: Composite Finite Elements for problems containing small geometric details. Part II: Implementation and numerical results. Comput. Visual Sci. 1(4), 15\u201325 (1997)","journal-title":"Computing and Visualization in Science"},{"issue":"4","key":"802_CR42","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/s002110050248","volume":"75","author":"W Hackbusch","year":"1997","unstructured":"Hackbusch, W., Sauter, S.A.: Composite Finite Elements for the approximation of PDEs on domains with complicated micro-structures. Numer. Math. 75(4), 447\u2013472 (1997)","journal-title":"Numer. Math."},{"issue":"9","key":"802_CR43","doi-asserted-by":"publisher","first-page":"1310","DOI":"10.1002\/nme.2123","volume":"73","author":"DJ Holdych","year":"2015","unstructured":"Holdych, D.J., Noble, D.R., Secor, R.B.: Quadrature rules for triangular and tetrahedral elements with generalized functions. Int. J. Numer. Methods Eng. 73(9), 1310\u20131327 (2015)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"1","key":"802_CR44","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1006\/jcph.1996.5633","volume":"132","author":"J Hyman","year":"1997","unstructured":"Hyman, J., Shashkov, M., Steinberg, S.: The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials. J. Comput. Phys. 132(1), 130\u2013148 (1997)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"802_CR45","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1137\/S1064827595287997","volume":"20","author":"G Karypis","year":"1998","unstructured":"Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359\u2013392 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"802_CR46","unstructured":"Karypis, G., Kumar, V.: Metis: Unstructured graph partitioning and sparse matrix ordering system, version 4.0. http:\/\/www.cs.umn.edu\/~metis (2009)"},{"issue":"8","key":"802_CR47","doi-asserted-by":"publisher","first-page":"2433","DOI":"10.1090\/S0002-9939-98-04454-2","volume":"126","author":"JB Lasserre","year":"1998","unstructured":"Lasserre, J.B.: Integration on a convex polytope. Proc. Am. Math. Soc. 126(8), 2433\u20132441 (1998)","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"802_CR48","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.cam.2009.07.017","volume":"233","author":"CJ Li","year":"2009","unstructured":"Li, C.J., Lambertu, P., Dagnino, C.: Numerical integration over polygons using an eight-node quadrilateral spline finite element. J. Comput. Appl. Math. 233(2), 279\u2013292 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"802_CR49","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1137\/0714018","volume":"14","author":"JN Lyness","year":"1977","unstructured":"Lyness, J.N., Monegato, G.: Quadrature rules for regions having regular hexagonal symmetry. SIAM J. Numer. Anal. 14(2), 283\u2013295 (1977)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"802_CR50","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1137\/0733048","volume":"33","author":"J Ma","year":"1996","unstructured":"Ma, J., Rokhlin, V., Wandzura, S.: Generalized Gaussian quadrature of systems of arbitrary functions. SIAM J. Numer. Anal. 33(3), 971\u2013996 (1996)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"802_CR51","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J","volume":"46","author":"N Mo\u00ebs","year":"1999","unstructured":"Mo\u00ebs, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131\u2013150 (1999)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"802_CR52","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s00466-010-0562-5","volume":"47","author":"SE Mousavi","year":"2011","unstructured":"Mousavi, S.E., Sukumar, N.: Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons. Comput. Mech. 47(5), 535\u2013554 (2011)","journal-title":"Comput. Mech."},{"issue":"1","key":"802_CR53","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1002\/nme.2759","volume":"82","author":"SE Mousavi","year":"2010","unstructured":"Mousavi, S.E., Xiao, H., Sukumar, N.: Generalized Gaussian quadrature rules on arbitrary polygons. Internat. J. Numer. Methods Eng. 82(1), 99\u2013113 (2010)","journal-title":"Internat. J. Numer. Methods Eng."},{"issue":"1","key":"802_CR54","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1002\/nme.2589","volume":"80","author":"S Natarajan","year":"2009","unstructured":"Natarajan, S., Bordas, S., Mahapatra, D.R.: Numerical integration over arbitrary polygonal domains based on Schwarz\u2013Christoffel conformal mapping. Int. J. Numer. Methods Eng. 80(1), 103\u2013134 (2009)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"802_CR55","volume-title":"Numerical Recipes 3rd Edition: The Art of Scientific Computing","author":"WH Press","year":"2007","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd edn. Cambridge University Press, New York (2007)","edition":"3"},{"key":"802_CR56","unstructured":"Qian, H.: Counting the floating point operations (flops). https:\/\/it.mathworks.com\/matlabcentral\/fileexchange\/50608-counting-the-floating-point-operations--flops- (2015)"},{"key":"802_CR57","volume-title":"Numerical Mathematics","author":"A Quarteroni","year":"2007","unstructured":"Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, Berlin (2007)"},{"key":"802_CR58","volume-title":"Mathematics for Economists","author":"CP Simon","year":"1996","unstructured":"Simon, C.P., Blume, L.E.: Mathematics for Economists. W. W. Norton and Company, New York (1996)"},{"issue":"2","key":"802_CR59","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s10543-007-0131-2","volume":"47","author":"A Sommariva","year":"2007","unstructured":"Sommariva, A., Vianello, M.: Product Gauss cubature over polygons based on Green\u2019s integration formula. BIT 47(2), 441\u2013453 (2007)","journal-title":"BIT"},{"issue":"2","key":"802_CR60","first-page":"138","volume":"47","author":"AH Stroud","year":"1967","unstructured":"Stroud, A.H., Secrest, D.: Gaussiam quadrature formulas. ZAMM Z. Angew. Math. Mech. 47(2), 138\u2013139 (1967)","journal-title":"ZAMM Z. Angew. Math. Mech."},{"issue":"1","key":"802_CR61","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.cma.2013.01.007","volume":"258","author":"Y Sudhakar","year":"2013","unstructured":"Sudhakar, Y., Wall, W.A.: Quadrature schemes for arbitrary convex\/concave volumes and integration of weak form in enriched partition of unity methods. Comput. Methods Appl. Mech. Eng. 258(1), 39\u201354 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"11","key":"802_CR62","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1002\/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A","volume":"48","author":"N Sukumar","year":"2000","unstructured":"Sukumar, N., Mo\u00ebs, N., Belytschko, T.: Extended Finite Element Method for three-dimensional crack modelling. Int. J. Numer. Methods Eng. 48(11), 1549\u20131570 (2000)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"12","key":"802_CR63","doi-asserted-by":"publisher","first-page":"2045","DOI":"10.1002\/nme.1141","volume":"61","author":"N Sukumar","year":"2004","unstructured":"Sukumar, N., Tabarraei, A.: Conforming polygonal finite elements. Int. J. Numer. Methods Eng. 61(12), 2045\u20132066 (2004)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"802_CR64","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1016\/j.cma.2007.08.013","volume":"197","author":"A Tabarraei","year":"2008","unstructured":"Tabarraei, A., Sukumar, N.: Extended Finite Element Method on polygonal and quadtree meshes. Comput. Methods Appl. Mech. Eng. 197(5), 425\u2013438 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"802_CR65","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s00158-011-0706-z","volume":"45","author":"C Talischi","year":"2012","unstructured":"Talischi, C., Paulino, G.H., Pereira, A., Menezes, I.F.M.: Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidiscip. Optim. 45(3), 309\u2013328 (2012)","journal-title":"Struct. Multidiscip. Optim."},{"key":"802_CR66","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9320-7","volume-title":"Partial Differential Equations: Basic Theory","author":"ME Taylor","year":"1996","unstructured":"Taylor, M.E.: Partial Differential Equations: Basic Theory. Springer, New York (1996)"},{"issue":"5","key":"802_CR67","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1002\/nme.1570","volume":"66","author":"G Ventura","year":"2006","unstructured":"Ventura, G.: On the elimination of quadrature subcells for discontinuous functions in the extended finite-element method. Int. J. Numer. Methods Eng. 66(5), 761\u2013795 (2006)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"3\u20134","key":"802_CR68","doi-asserted-by":"publisher","first-page":"688","DOI":"10.1002\/nme.4679","volume":"102","author":"G Ventura","year":"2015","unstructured":"Ventura, G., Benvenuti, E.: Equivalent polynomials for quadrature in Heaviside function enriched elements. Int. J. Numer. Methods Eng. 102(3\u20134), 688\u2013710 (2015)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"2","key":"802_CR69","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/j.camwa.2009.10.027","volume":"59","author":"H Xiao","year":"2010","unstructured":"Xiao, H., Gimbutas, Z.: A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions. Comput. Math. Appl. 59(2), 663\u2013676 (2010)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"802_CR70","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1137\/S1064827596310779","volume":"20","author":"N Yarvin","year":"1998","unstructured":"Yarvin, N., Rokhlin, V.: Generalized Gaussian quadratures and singular value decompositions of integral operators. SIAM J. Sci. Comput. 20(2), 669\u2013718 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"16","key":"802_CR71","first-page":"104","volume":"10","author":"AM Yogitha","year":"2016","unstructured":"Yogitha, A.M., Shivaram, K.T.: Numerical integration of arbitrary functions over a convex and non convex polygonal domain by eight noded linear quadrilateral finite element method. Aust. J. Basic Appl. Sci. 10(16), 104\u2013110 (2016)","journal-title":"Aust. J. Basic Appl. Sci."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0802-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0802-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0802-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,8]],"date-time":"2020-11-08T13:04:01Z","timestamp":1604840641000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0802-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,29]]},"references-count":71,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["802"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0802-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,29]]},"assertion":[{"value":"12 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}