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 162 articles )

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  1. Atallah, Nabil M.; Canuto, Claudio; Scovazzi, Guglielmo: Analysis of the shifted boundary method for the Poisson problem in domains with corners (2021)
  2. Badia, Santiago; Martín, Alberto F.; Neiva, Eric; Verdugo, Francesc: The aggregated unfitted finite element method on parallel tree-based adaptive meshes (2021)
  3. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  4. Burman, Erik; Cicuttin, Matteo; Delay, Guillaume; Ern, Alexandre: An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems (2021)
  5. Burman, Erik; He, Cuiyu; Larson, Mats G.: Comparison of shape derivatives using CutFEM for ill-posed Bernoulli free boundary problem (2021)
  6. Cai, Ying; Chen, Jinru; Wang, Nan: A Nitsche extended finite element method for the biharmonic interface problem (2021)
  7. Chin, Eric B.; Sukumar, N.: Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries (2021)
  8. Dsouza, Shaima M.; Pramod, A. L. N.; Ooi, Ean Tat; Song, Chongmin; Natarajan, Sundararajan: Robust modelling of implicit interfaces by the scaled boundary finite element method (2021)
  9. Dunn, Kyle; Lui, Roger; Sarkis, Marcus: An unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid (2021)
  10. Engwer, Christian; Westerheide, Sebastian: An unfitted dG scheme for coupled bulk-surface PDEs on complex geometries (2021)
  11. Gfrerer, Michael H.: A (C^1)-continuous trace-finite-cell-method for linear thin shell analysis on implicitly defined surfaces (2021)
  12. Guo, Hailong; Yang, Xu; Zhu, Yi: Unfitted Nitsche’s method for computing band structures of phononic crystals with periodic inclusions (2021)
  13. Guo, Hailong; Yang, Xu; Zhu, Yi: Unfitted Nitsche’s method for computing wave modes in topological materials (2021)
  14. Guo, Ruchi: Solving parabolic moving interface problems with dynamical immersed spaces on unfitted meshes: fully discrete analysis (2021)
  15. Guo, Ruchi; Lin, Tao; Lin, Yanping; Zhuang, Qiao: Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems (2021)
  16. Hakula, Harri; Nasyrov, Semen; Vuorinen, Matti: Conformal moduli of symmetric circular quadrilaterals with cusps (2021)
  17. Jin, Mengqing; Feng, Xinlong; Wang, Kun: Gradient recovery-based adaptive stabilized mixed FEM for the convection-diffusion-reaction equation on surfaces (2021)
  18. Neiva, Eric; Badia, Santiago: Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems (2021)
  19. Olshanskii, Maxim A.; Reusken, Arnold; Zhiliakov, Alexander: Inf-sup stability of the trace (\mathbfP_2-P_1) Taylor-Hood elements for surface PDEs (2021)
  20. Olshanskii, Maxim; Quaini, Annalisa; Sun, Qi: An unfitted finite element method for two-phase Stokes problems with slip between phases (2021)

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