CutFEM: Discretizing geometry and partial differential equations. We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.

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  1. Aragón, Alejandro M.; Liang, Bowen; Ahmadian, Hossein; Soghrati, Soheil: On the stability and interpolating properties of the hierarchical interface-enriched finite element method (2020)
  2. Atallah, Nabil M.; Canuto, Claudio; Scovazzi, Guglielmo: Analysis of the shifted boundary method for the Stokes problem (2020)
  3. Bui, Hoang-Giang; Schillinger, Dominik; Meschke, Günther: Efficient cut-cell quadrature based on moment fitting for materially nonlinear analysis (2020)
  4. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Massing, André; Zahedi, Sara: A stabilized cut streamline diffusion finite element method for convection-diffusion problems on surfaces (2020)
  5. Chernyshenko, Alexey Y.; Olshanskii, Maxim A.: An unfitted finite element method for the Darcy problem in a fracture network (2020)
  6. Duprez, Michel; Lozinski, Alexei: (\phi)-FEM: a finite element method on domains defined by level-sets (2020)
  7. Fries, T. P.; Schöllhammer, D.: A unified finite strain theory for membranes and ropes (2020)
  8. Giani, Stefano: An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients (2020)
  9. Liu, Huaqing; Zhang, Linbo; Zhang, Xiaodi; Zheng, Weiying: Interface-penalty finite element methods for interface problems in (H^1), (\boldsymbolH(\mathbfcurl)), and (\boldsymbolH(\operatornamediv)) (2020)
  10. Ludescher, Thomas; Gross, Sven; Reusken, Arnold: A multigrid method for unfitted finite element discretizations of elliptic interface problems (2020)
  11. Lu, Kaizhou; Coombs, William M.; Augarde, Charles E.; Hu, Zhendong: An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses (2020)
  12. Oyarzúa, Ricardo; Solano, Manuel; Zúñiga, Paulo: A priori and a posteriori error analyses of a high order unfitted mixed-FEM for Stokes flow (2020)
  13. Sun, Haohan; Schillinger, Dominik; Yuan, Si: Implicit a posteriori error estimation in cut finite elements (2020)
  14. Wang, Tao; Yang, Chaochao; Xie, Xiaoping: A Nitsche-extended finite element method for distributed optimal control problems of elliptic interface equations (2020)
  15. Ager, C.; Schott, B.; Winter, M.; Wall, W. A.: A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity (2019)
  16. Albella, Jorge; Ben Dhia, Hachmi; Imperiale, Sebastien; Rodríguez, Jeronimo: Mathematical and numerical study of transient wave scattering by obstacles with a new class of Arlequin coupling (2019)
  17. Andreas Nüßing, Maria Carla Piastra, Sophie Schrader, Tuuli Miinalainen, Heinrich Brinck, Carsten H. Wolters, Christian Engwer: duneuro - A software toolbox for forward modeling in neuroscience (2019) arXiv
  18. Antolin, Pablo; Buffa, Annalisa; Martinelli, Massimiliano: Isogeometric analysis on V-reps: first results (2019)
  19. Bansal, Manik; Singh, I. V.; Mishra, B. K.; Bordas, S. P. A.: A parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials (2019)
  20. Bansal, Manik; Singh, I. V.; Patil, R. U.; Claus, Susanne; Bordas, S. P. A.: A simple and robust computational homogenization approach for heterogeneous particulate composites (2019)

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