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 112 articles )

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  1. Harari, Isaac; Albocher, Uri: Complementary solutions of Nitsche’s method (2019)
  2. Henyš, Petr; Čapek, Lukáš; Březina, Jan: Comparison of current methods for implementing periodic boundary conditions in multi-scale homogenisation (2019)
  3. Johansson, August; Kehlet, Benjamin; Larson, Mats G.; Logg, Anders: Multimesh finite element methods: solving PDEs on multiple intersecting meshes (2019)
  4. Jonsson, Tobias; Larson, Mats G.; Larsson, Karl: Graded parametric CutFEM and CutIGA for elliptic boundary value problems in domains with corners (2019)
  5. Lehrenfeld, Christoph; Olshanskii, Maxim: An Eulerian finite element method for PDEs in time-dependent domains (2019)
  6. Leichner, Alexander; Andrä, Heiko; Simeon, Bernd: A contact algorithm for voxel-based meshes using an implicit boundary representation (2019)
  7. Lozinski, Alexei: CutFEM without cutting the mesh cells: a new way to impose Dirichlet and Neumann boundary conditions on unfitted meshes (2019)
  8. Mu, Lin; Zhang, Xu: An immersed weak Galerkin method for elliptic interface problems (2019)
  9. Nguyen, Lam H.; Schillinger, Dominik: A residual-driven local iterative corrector scheme for the multiscale finite element method (2019)
  10. Odsæter, Lars H.; Kvamsdal, Trond; Larson, Mats G.: A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media (2019)
  11. Schöllhammer, D.; Fries, T. P.: Reissner-Mindlin shell theory based on tangential differential calculus (2019)
  12. Schöllhammer, D.; Fries, T. P.: Kirchhoff-Love shell theory based on tangential differential calculus (2019)
  13. Simon, K.; Tobiska, L.: Local projection stabilization for convection-diffusion-reaction equations on surfaces (2019)
  14. Sticko, Simon; Kreiss, Gunilla: Higher order cut finite elements for the wave equation (2019)
  15. Zhuang, Qiao; Guo, Ruchi: High degree discontinuous Petrov-Galerkin immersed finite element methods using fictitious elements for elliptic interface problems (2019)
  16. Badia, Santiago; Martin, Alberto F.; Verdugo, Francesc: Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem (2018)
  17. Badia, Santiago; Verdugo, Francesc: Robust and scalable domain decomposition solvers for unfitted finite element methods (2018)
  18. Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.: The aggregated unfitted finite element method for elliptic problems (2018)
  19. Boiveau, Thomas; Burman, Erik; Claus, Susanne; Larson, Mats: Fictitious domain method with boundary value correction using penalty-free Nitsche method (2018)
  20. Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G.; Larsson, Karl: Shape optimization using the cut finite element method (2018)