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.

References in zbMATH (referenced in 58 articles )

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  1. Ludescher, Thomas; Gross, Sven; Reusken, Arnold: A multigrid method for unfitted finite element discretizations of elliptic interface problems (2020)
  2. 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)
  3. 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
  4. Bezchlebová, Eva; Dolejší, Vít; Feistauer, Miloslav; Sváček, Petr: Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods (2019)
  5. Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G.; Larsson, Karl: Hybridized CutFEM for elliptic interface problems (2019)
  6. Burman, Erik; Hansbo, Peter; Larson, Mats G.: A simple finite element method for elliptic bulk problems with embedded surfaces (2019)
  7. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Larsson, Karl: Cut finite elements for convection in fractured domains (2019)
  8. 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)
  9. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Samvin, David: A cut finite element method for elliptic bulk problems with embedded surfaces (2019)
  10. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Zahedi, Sara: Stabilized CutFEM for the convection problem on surfaces (2019)
  11. Cao, Shuhao; Chen, Long: Anisotropic error estimates of the linear nonconforming virtual element methods (2019)
  12. Dokken, Jørgen S.; Funke, Simon W.; Johansson, August; Schmidt, Stephan: Shape optimization using the finite element method on multiple meshes with Nitsche coupling (2019)
  13. Duprez, Michel; Lleras, Vanessa; Lozinski, Alexei: Finite element method with local damage of the mesh (2019)
  14. Guo, Ruchi; Lin, Tao: A higher degree immersed finite element method based on a Cauchy extension for elliptic interface problems (2019)
  15. Harari, Isaac; Albocher, Uri: Complementary solutions of Nitsche’s method (2019)
  16. Lehrenfeld, Christoph; Olshanskii, Maxim: An Eulerian finite element method for PDEs in time-dependent domains (2019)
  17. Mu, Lin; Zhang, Xu: An immersed weak Galerkin method for elliptic interface problems (2019)
  18. Nguyen, Lam H.; Schillinger, Dominik: A residual-driven local iterative corrector scheme for the multiscale finite element method (2019)
  19. Schöllhammer, D.; Fries, T. P.: Kirchhoff-Love shell theory based on tangential differential calculus (2019)
  20. Sticko, Simon; Kreiss, Gunilla: Higher order cut finite elements for the wave equation (2019)

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