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.

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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. 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)
  6. 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)
  7. Gfrerer, Michael H.: A (C^1)-continuous trace-finite-cell-method for linear thin shell analysis on implicitly defined surfaces (2021)
  8. Guo, Ruchi: Solving parabolic moving interface problems with dynamical immersed spaces on unfitted meshes: fully discrete analysis (2021)
  9. 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)
  10. Olshanskii, Maxim A.; Reusken, Arnold; Zhiliakov, Alexander: Inf-sup stability of the trace (\mathbfP_2-P_1) Taylor-Hood elements for surface PDEs (2021)
  11. Olshanskii, Maxim; Xu, Xianmin; Yushutin, Vladimir: A finite element method for Allen-Cahn equation on deforming surface (2021)
  12. Ospald, Felix; Bergermann, Kai; Herzog, Roland: An extension of the strain transfer principle for fiber reinforced materials (2021)
  13. Rouwane, Ali; Bouclier, Robin; Passieux, Jean-Charles; Périé, Jean-Noël: Adjusting fictitious domain parameters for fairly priced image-based modeling: application to the regularization of digital image correlation (2021)
  14. Shakour, Emad; Amir, Oded: Topology optimization with precise evolving boundaries based on IGA and untrimming techniques (2021)
  15. Zhu, Lixing; Masud, Arif: Variationally derived interface stabilization for discrete multiphase flows and relation with the ghost-penalty method (2021)
  16. Alberto Paganini, Florian Wechsung: Fireshape: a shape optimization toolbox for Firedrake (2020) arXiv
  17. Aragón, Alejandro M.; Liang, Bowen; Ahmadian, Hossein; Soghrati, Soheil: On the stability and interpolating properties of the hierarchical interface-enriched finite element method (2020)
  18. Atallah, Nabil M.; Canuto, Claudio; Scovazzi, Guglielmo: The second-generation shifted boundary method and its numerical analysis (2020)
  19. Atallah, Nabil M.; Canuto, Claudio; Scovazzi, Guglielmo: Analysis of the shifted boundary method for the Stokes problem (2020)
  20. Brandner, Philip; Reusken, Arnold: Finite element error analysis of surface Stokes equations in stream function formulation (2020)

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