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 204 articles )

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  1. Antolin, Pablo; Wei, Xiaodong; Buffa, Annalisa: Robust numerical integration on curved polyhedra based on folded decompositions (2022)
  2. Aretaki, Aikaterini; Karatzas, Efthymios N.: Random geometries for optimal control PDE problems based on fictitious domain FEMs and cut elements (2022)
  3. Atallah, Nabil M.; Canuto, Claudio; Scovazzi, Guglielmo: The high-order shifted boundary method and its analysis (2022)
  4. Badia, Santiago; Martorell, Pere A.; Verdugo, Francesc: Geometrical discretisations for unfitted finite elements on explicit boundary representations (2022)
  5. Barbeau, Lucka; Étienne, Stéphane; Béguin, Cédric; Blais, Bruno: Development of a high-order continuous Galerkin sharp-interface immersed boundary method and its application to incompressible flow problems (2022)
  6. Burman, Erik; Duran, Omar; Ern, Alexandre: Unfitted hybrid high-order methods for the wave equation (2022)
  7. Burman, Erik; Frei, Stefan; Massing, Andre: Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains (2022)
  8. Burman, Erik; Hansbo, Peter; Larson, Mats G.: Explicit time stepping for the wave equation using CutFEM with discrete extension (2022)
  9. Garhuom, Wadhah; Usman, Khuldoon; Düster, Alexander: An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems (2022)
  10. Gulizzi, Vincenzo; Saye, Robert: Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods (2022)
  11. Guo, Hailong; Yang, Xu: Deep unfitted Nitsche method for elliptic interface problems (2022)
  12. Hansbo, Peter; Larson, Mats G.: Nitsche’s finite element method for model coupling in elasticity (2022)
  13. Hartmann, Frank; Kollmannsberger, Stefan: Enforcing essential boundary conditions on domains defined by point clouds (2022)
  14. He, Cuiyu; Hu, Xiaozhe; Mu, Lin: A mesh-free method using piecewise deep neural network for elliptic interface problems (2022)
  15. He, Xiaoxiao; Deng, Weibing: An interface penalty parameter free nonconforming cut finite element method for elliptic interface problems (2022)
  16. Huang, Junjie; Deng, Fangqian; Liu, Lingfei; Ye, Jianqiao: Adaptive stochastic morphology simulation and mesh generation of high-quality 3D particulate composite microstructures with complex surface texture (2022)
  17. Jiang, Wen; Liu, Yingjie; Annavarapu, Chandrasekhar: A weighted Nitsche’s method for interface problems with higher-order simplex elements (2022)
  18. Kadapa, Chennakesava: A unified simulation framework for fluid-structure-control interaction problems with rigid and flexible structures (2022)
  19. Kees, Christopher E.; Collins, J. Haydel; Zhang, Alvin: Simple, accurate, and efficient embedded finite element methods for fluid-solid interaction (2022)
  20. King, J. R. C.; Lind, S. J.: High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM) (2022)

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