Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 316 (2017) 400–423 www.elsevier.com/locate/cma Mixed Isogeometric Finite Cell Methods for the Stokes problem Tuong Hoang a,b,∗ , ClemensV. Verhoosel b , Ferdinando Auricchio c , E. Harald van Brummelen b , Alessandro Reali c,d a Scuola Universitaria Superiore IUSS Pavia, 27100 Pavia, Italy b Department of Mechanical Engineering, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands c Department of Civil Engineering and Architecture, University of Pavia, 27100 Pavia, Italy d Technische Universit¨ at M¨ unchen – Institute for Advanced Study, 85748 Garching, Germany Available online 4 August 2016 Highlights • The application of the Isogeometric Finite Cell Method to mixed formulations is studied. • The performance of four families of isogeometric mixed finite elements is compared. • For all considered elements the inf–sup stability is tested using a generic Stokes test case. • A detailed mesh convergence study is performed to assess the optimality of all elements. Abstract We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor–Hood, Sub-grid, Raviart–Thomas, and N´ ed´ elec elements. These element families have been demonstrated to perform well in the case of conforming meshes, but their applicability in the cut-cell context is still unclear. Dirichlet boundary conditions are imposed by Nitsche’s method. Numerical test problems are performed, with a detailed study of the discrete inf–sup stability constants and of the convergence behavior under uniform mesh refinement. c ⃝ 2016 Elsevier B.V. All rights reserved. Keywords: Isogeometric analysis; Finite cell method; Immersed boundary method; Fictitious domain; Mixed formulations; Stokes 1. Introduction Isogeometric analysis (IGA) was proposed in [1] as a framework to reduce the gap between Computer Aided Design (CAD) and Finite Element Analysis (FEA). The fundamental idea of IGA is to employ the same basis functions to describe both the geometry of the domain of interest and the field variables. In contrast to conventional FEA which typically uses Lagrange polynomials as basis functions, IGA utilizes basis functions inherited from ∗ Corresponding author at: Scuola Universitaria Superiore IUSS Pavia, 27100 Pavia, Italy. E-mail addresses: tuong.hoang@iusspavia.it, t.hoang@tue.nl (T. Hoang). http://dx.doi.org/10.1016/j.cma.2016.07.027 0045-7825/ c ⃝ 2016 Elsevier B.V. All rights reserved.