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 19 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. Guo, Hailong; Yang, Xu: Gradient recovery for elliptic interface problem. III: Nitsche’s method (2018)
  4. Xu, Shipeng; Deng, Weibing; Wu, Haijun: A combined finite element method for elliptic problems posted in domains with rough boundaries (2018)
  5. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)
  6. Chernyshenko, Alexey; Olshahskii, Maxim; Vassilevski, Yuri: A hybrid finite volume -- finite element method for modeling flows in fractured media (2017)
  7. Ji, Haifeng; Wang, Feng; Chen, Jinru: Unfitted finite element methods for the heat conduction in composite media with contact resistance (2017)
  8. Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin; Shashkov, Mikhail: Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces (2017)
  9. Lehrenfeld, Christoph; Reusken, Arnold: High order unfitted finite element methods for interface problems and PDEs on surfaces (2017)
  10. Quarteroni, A.; Manzoni, A.; Vergara, C.: The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications (2017)
  11. Saye, Robert: Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow. I (2017)
  12. Zheng, Hong; Li, Wei; Du, Xiuli: Exact imposition of essential boundary condition and material interface continuity in Galerkin-based meshless methods (2017)
  13. Burman, Erik; Hansbo, Peter; Larson, Mats G.; Zahedi, Sara: Cut finite element methods for coupled bulk-surface problems (2016)
  14. Fries, Thomas-Peter; Omerović, Samir: Higher-order accurate integration of implicit geometries (2016)
  15. Gross, Sven; Ludescher, Thomas; Olshanskii, Maxim; Reusken, Arnold: Robust preconditioning for XFEM applied to time-dependent Stokes problems (2016)
  16. 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)
  17. Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, André: CutFEM: discretizing geometry and partial differential equations (2015)
  18. Burman, Erik; Claus, Susanne; Massing, André: A stabilized cut finite element method for the three field Stokes problem (2015)
  19. Dolbow, John (ed.); Farhat, Charbel (ed.); Harari, Isaac (ed.); Lew, Adrian (ed.): Special issue: Advances in embedded interface methods (2015)