Abedian, AlirezaAlirezaAbedianParvizian, JamshidJamshidParvizianDüster, AlexanderAlexanderDüsterKhademyzadeh, HassanHassanKhademyzadehRank, ErnstErnstRank2020-07-162020-07-162013-02-18International Journal of Computational Methods 3 (10): 1350002 (2013)http://hdl.handle.net/11420/6843In many extended versions of the finite element method (FEM) the mesh does not conform to the physical domain. Therefore, discontinuity of variables is expected when some elements are cut by the boundary. Thus, the integrands are not continuous over the whole integration domain. Apparently, none of the well developed integration schemes such as Gauss quadrature can be used readily. This paper investigates several modifications of the Gauss quadrature to capture the discontinuity within an element and to perform a more precise integration. The extended method used here is the finite cell method (FCM), an extension of a high-order approximation space with the aim of simple meshing. Several examples are included to evaluate different modifications. © 2013 World Scientific Publishing Company.en0219-876220133World Scientific Publishingdiscontinuous integrationFinite cell methodGauss quadratureoctreequadtreeIngenieurwissenschaftenJournal Article10.1142/S0219876213500023Other