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 12 articles )

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  1. Burman, Erik; Hansbo, Peter; Larson, Mats G.: A cut finite element method with boundary value correction (2018)
  2. Chernyshenko, Alexey Y.; Olshanskii, Maxim A.; Vassilevski, Yuri V.: A hybrid finite volume -- finite element method for bulk-surface coupled problems (2018)
  3. Chernyshenko, Alexey; Olshahskii, Maxim; Vassilevski, Yuri: A hybrid finite volume -- finite element method for modeling flows in fractured media (2017)
  4. Ji, Haifeng; Wang, Feng; Chen, Jinru: Unfitted finite element methods for the heat conduction in composite media with contact resistance (2017)
  5. Zheng, Hong; Li, Wei; Du, Xiuli: Exact imposition of essential boundary condition and material interface continuity in Galerkin-based meshless methods (2017)
  6. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Zahedi, Sara: Cut finite element methods for coupled bulk-surface problems (2016)
  7. Fries, Thomas-Peter; Omerović, Samir: Higher-order accurate integration of implicit geometries (2016)
  8. Gross, Sven; Ludescher, Thomas; Olshanskii, Maxim; Reusken, Arnold: Robust preconditioning for XFEM applied to time-dependent Stokes problems (2016)
  9. Safdari, Masoud; Najafi, Ahmad R.; Sottos, Nancy R.; Geubelle, Philippe H.: A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials (2016)
  10. Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, André: CutFEM: discretizing geometry and partial differential equations (2015)
  11. Burman, Erik; Claus, Susanne; Massing, André: A stabilized cut finite element method for the three field Stokes problem (2015)
  12. Dolbow, John (ed.); Farhat, Charbel (ed.); Harari, Isaac (ed.); Lew, Adrian (ed.): Special issue: Advances in embedded interface methods (2015)