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Recent Developments in Unfitted Finite Element Methods: Numerical Analysis, High-Performance Adaptive Solution Algorithms and Advanced Digital Pipelines

Guest Editors: 

  • Pierre Kerfriden (Centre des Matériaux, Mines ParisTech & PSL University, Corbeil-Essonnes, France)
  • Susanne Claus (Applied Mathematics and Scientific Computation group, ONERA, Palaiseau, France)
  • André Massing (Department of Mathematical Sciences, NTNU – Norwegian University of Science and Technology, Norway)
  • Dominik Schillinger (Institute of Mechanics and Computational Mechanics, Leibniz Universität Hannover, Hanover, Germany)

Unfitted Finite Element Methods (UFEM e.g. CutFEM, XFEM, Finite Cell FEM, CGFEM) have been extensively investigated over the last two decades. The use of computational meshes that do not need to conform to the geometrical features of boundary value problems is highly interesting to practitioners in many fields of computational sciences and engineering. However, UFEM are yet to be adopted as a standard analysis tool. This is due to a number of important theoretical, implementational and numerical challenges, which we wish to address in this special issue.


  1. This paper presents a robust digital pipeline from CT images to the simulation of contact between multiple bodies. The proposed strategy relies on a recently developed immersed finite element algorithm that is...

    Authors: S. Claus, P. Kerfriden, F. Moshfeghifar, S. Darkner, K. Erleben and C. Wong
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2021 8:13
    Content type: Research article Published on:

  2. A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, ...

    Authors: Sofia Farina, Susanne Claus, Jack S. Hale, Alexander Skupin and Stéphane P. A. Bordas
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2021 8:5
    Content type: Research article Published on:

  3. This paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new mod...

    Authors: Benjamin Wassermann, Nina Korshunova, Stefan Kollmannsberger, Ernst Rank and Gershon Elber
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:49
    Content type: Research article Published on:

  4. A new specialised finite element for simulating the cracking and healing behaviour of quasi-brittle materials is presented. The element employs a strong discontinuity approach to represent displacement jumps a...

    Authors: Brubeck L. Freeman, Pedro Bonilla-Villalba, Iulia C. Mihai, Waled F. Alnaas and Anthony D. Jefferson
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:32
    Content type: Research article Published on:

  6. In the present work, we propose a new approach, the so-called compressed adaptive integration scheme (C-AIS), for the computation of the stiffness and mass matrices in fictitious domain methods requiring the i...

    Authors: Márton Petö, Fabian Duvigneau and Sascha Eisenträger
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:21
    Content type: Research article Published on:

    The Correction to this article has been published in Advanced Modeling and Simulation in Engineering Sciences 2020 7:34

  7. We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The f...

    Authors: P. Kerfriden, S. Claus and I. Mihai
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:18
    Content type: Research article Published on: