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. 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
  2. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Larsson, Karl; Massing, André: Finite element approximation of the Laplace-Beltrami operator on a surface with boundary (2019)
  3. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Zahedi, Sara: Stabilized CutFEM for the convection problem on surfaces (2019)
  4. Badia, Santiago; Martin, Alberto F.; Verdugo, Francesc: Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem (2018)
  5. Badia, Santiago; Verdugo, Francesc: Robust and scalable domain decomposition solvers for unfitted finite element methods (2018)
  6. Boiveau, Thomas; Burman, Erik; Claus, Susanne; Larson, Mats: Fictitious domain method with boundary value correction using penalty-free Nitsche method (2018)
  7. Burman, Erik; Ern, Alexandre: An unfitted hybrid high-order method for elliptic interface problems (2018)
  8. Burman, Erik; Hansbo, Peter; Larson, Mats G.: A cut finite element method with boundary value correction (2018)
  9. Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Younis A.: Adaptive discontinuous Galerkin methods for elliptic interface problems (2018)
  10. Carraro, Thomas; Dörsam, Simon; Frei, Stefan; Schwarz, Daniel: An adaptive Newton algorithm for optimal control problems with application to optimal electrode design (2018)
  11. Chernyshenko, Alexey Y.; Olshanskii, Maxim A.; Vassilevski, Yuri V.: A hybrid finite volume -- finite element method for bulk-surface coupled problems (2018)
  12. Claus, Susanne; Bigot, Samuel; Kerfriden, Pierre: CutFEM method for Stefan-Signorini problems with application in pulsed laser ablation (2018)
  13. Guo, Hailong; Yang, Xu: Gradient recovery for elliptic interface problem. III: Nitsche’s method (2018)
  14. Guzmán, Johnny; Olshanskii, Maxim: Inf-sup stability of geometrically unfitted Stokes finite elements (2018)
  15. Kikinzon, Evgeny; Shashkov, Mikhail; Garimella, Rao: Establishing mesh topology in multi-material cells: enabling technology for robust and accurate multi-material simulations (2018)
  16. Ludvigsson, Gustav; Steffen, Kyle R.; Sticko, Simon; Wang, Siyang; Xia, Qing; Epshteyn, Yekaterina; Kreiss, Gunilla: High-order numerical methods for 2D parabolic problems in single and composite domains (2018)
  17. Nüßing, Andreas: Fitted and unfitted finite element methods for solving the EEG forward problem (2018)
  18. Xu, Shipeng; Deng, Weibing; Wu, Haijun: A combined finite element method for elliptic problems posted in domains with rough boundaries (2018)
  19. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)
  20. Chernyshenko, Alexey; Olshahskii, Maxim; Vassilevski, Yuri: A hybrid finite volume -- finite element method for modeling flows in fractured media (2017)

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