Relevant bibliographies by topics / Unfitted Finite Elements

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Unfitted Finite Elements'

Author: Grafiati
Published: 4 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Unfitted Finite Elements"

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Formaggia, Luca, Christian Vergara, and Stefano Zonca. "Unfitted extended finite elements for composite grids." Computers & Mathematics with Applications 76, no. 4 (2018): 893–904. http://dx.doi.org/10.1016/j.camwa.2018.05.028.

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Guzmán, Johnny, and Maxim Olshanskii. "Inf-sup stability of geometrically unfitted Stokes finite elements." Mathematics of Computation 87, no. 313 (2017): 2091–112. http://dx.doi.org/10.1090/mcom/3288.

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Badia, Santiago, Pere A. Martorell, and Francesc Verdugo. "Geometrical discretisations for unfitted finite elements on explicit boundary representations." Journal of Computational Physics 460 (July 2022): 111162. http://dx.doi.org/10.1016/j.jcp.2022.111162.

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Badia, Santiago, Pere A. Martorell, and Francesc Verdugo. "Space–time unfitted finite elements on moving explicit geometry representations." Computer Methods in Applied Mechanics and Engineering 428 (August 2024): 117091. http://dx.doi.org/10.1016/j.cma.2024.117091.

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Dziuk, Gerhard, and Charles M. Elliott. "Finite element methods for surface PDEs." Acta Numerica 22 (April 2, 2013): 289–396. http://dx.doi.org/10.1017/s0962492913000056.

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In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with il
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Badia, Santiago, Eric Neiva, and Francesc Verdugo. "Robust high-order unfitted finite elements by interpolation-based discrete extension." Computers & Mathematics with Applications 127 (December 2022): 105–26. http://dx.doi.org/10.1016/j.camwa.2022.09.027.

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Burman, Erik, Peter Hansbo, Mats G. Larson, and Sara Zahedi. "Cut finite element methods." Acta Numerica 34 (July 2025): 1–121. https://doi.org/10.1017/s0962492925000017.

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Cut finite element methods (CutFEM) extend the standard finite element method to unfitted meshes, enabling the accurate resolution of domain boundaries and interfaces without requiring the mesh to conform to them. This approach preserves the key properties and accuracy of the standard method while addressing challenges posed by complex geometries and moving interfaces.In recent years, CutFEM has gained significant attention for its ability to discretize partial differential equations in domains with intricate geometries. This paper provides a comprehensive review of the core concepts and key d
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Burman, Erik, and Janosch Preuss. "Unique continuation for an elliptic interface problem using unfitted isoparametric finite elements." SMAI Journal of computational mathematics 11 (March 24, 2025): 165–202. https://doi.org/10.5802/smai-jcm.122.

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Wegert, Zachary J., Jordi Manyer, Connor N. Mallon, Santiago Badia, and Vivien J. Challis. "Level-set topology optimisation with unfitted finite elements and automatic shape differentiation." Computer Methods in Applied Mechanics and Engineering 445 (October 2025): 118203. https://doi.org/10.1016/j.cma.2025.118203.

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Neiva, Eric, and Santiago Badia. "Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems." Computer Methods in Applied Mechanics and Engineering 380 (July 2021): 113769. http://dx.doi.org/10.1016/j.cma.2021.113769.

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Dissertations / Theses on the topic "Unfitted Finite Elements"

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Miranda, Neiva Eric. "Large-scale tree-based unfitted finite elements for metal additive manufacturing." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669823.

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This thesis addresses large-scale numerical simulations of partial differential equations posed on evolving geometries. Our target application is the simulation of metal additive manufacturing (or 3D printing) with powder-bed fusion methods, such as Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) or Electron-Beam Melting (EBM). The simulation of metal additive manufacturing processes is a remarkable computational challenge, because processes are characterised by multiple scales in space and time and multiple complex physics that occur in intricate three-dimensional growing-i
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Swift, Luke James. "Geometrically unfitted finite element methods for the Helmholtz equation." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10042813/.

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It is well known that the standard Galerkin finite element method experiences difficulties when applied to the Helmholtz equation in the medium to high wave number regime unless a condition of the form hk^2 < C is satisfied, where h is the mesh parameter and k is the wave number. This condition becomes even more difficult to enforce when coupling multiple domains which may have different wave numbers. Numerous stabilizations have been proposed in order to make computations under the engineering rule of thumb hk < C feasible. In this work I introduce a theoretical framework for analysing a clas
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Holmberg, Carl. "Cut finite element methods for incompressibleflows with unfitted interfaces." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151106.

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Problems with time-evolving domains are frequently occurring in computationalfluid dynamics and many other fields of science and engineering.Unfitted methods, where the computational mesh does not conform to thegeometry, are of great interest for handling such problems, since they removethe burden of mesh generation. We work towards the goal of developingan unfitted solver for Navier-Stokes equations on time-evolving domainsby developing and presenting cut finite element (CutFEM) splitting methodsfor solving Navier-Stokes equations. These CutFEM splitting methodsuse Nitsche’s method for incorp
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Nüßing, Andreas Verfasser], and Christian [Akademischer Betreuer] [Engwer. "Fitted and unfitted finite element methods for solving the EEG forward problem / Andreas Nüßing ; Betreuer: Christian Engwer." Münster : Universitäts- und Landesbibliothek Münster, 2018. http://d-nb.info/1167857291/34.

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Nüßing, Andreas [Verfasser], and Christian [Akademischer Betreuer] Engwer. "Fitted and unfitted finite element methods for solving the EEG forward problem / Andreas Nüßing ; Betreuer: Christian Engwer." Münster : Universitäts- und Landesbibliothek Münster, 2018. http://nbn-resolving.de/urn:nbn:de:hbz:6-67139436770.

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Guo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.

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This dissertation consists of three studies of immersed finite element (IFE) methods for inter- face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to elasticity systems, new breakthroughs to higher degree IFE methods, and its application to inverse problems. First, we extend the current construction and analysis approach of IFE methods in the literature for scalar elliptic equations to elasticity systems in the vector format. In particular, we cons
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Books on the topic "Unfitted Finite Elements"

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Bordas, Stéphane P. A., Erik Burman, Mats G. Larson, and Maxim A. Olshanskii, eds. Geometrically Unfitted Finite Element Methods and Applications. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71431-8.

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Larson, Mats G., Stéphane P. A. Bordas, Erik Burman, and Maxim A. Olshanskii. Geometrically Unfitted Finite Element Methods and Applications: Proceedings of the UCL Workshop 2016. Springer, 2018.

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Larson, Mats G., Stéphane P. A. Bordas, Erik Burman, and Maxim A. Olshanskii. Geometrically Unfitted Finite Element Methods and Applications: Proceedings of the UCL Workshop 2016. Springer, 2018.

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Book chapters on the topic "Unfitted Finite Elements"

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Heimann, Fabian, and Christoph Lehrenfeld. "Numerical Integration on Hyperrectangles in Isoparametric Unfitted Finite Elements." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-96415-7_16.

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Burman, Erik, and Peter Hansbo. "Deriving Robust Unfitted Finite Element Methods from Augmented Lagrangian Formulations." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71431-8_1.

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Lehrenfeld, Christoph, and Arnold Reusken. "High Order Unfitted Finite Element Methods for Interface Problems and PDEs on Surfaces." In Transport Processes at Fluidic Interfaces. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56602-3_2.

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Heimann, Fabian. "A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk Problems." In Lecture Notes in Computational Science and Engineering. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-86173-4_43.

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Fournié, Michel, and Alexei Lozinski. "Stability and Optimal Convergence of Unfitted Extended Finite Element Methods with Lagrange Multipliers for the Stokes Equations." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71431-8_5.

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Conference papers on the topic "Unfitted Finite Elements"

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Kothari, H., and R. Krause. "Multigrid and Saddle-Point Preconditioners for Unfitted Finite Element Modelling of Inclusions." In 14th WCCM-ECCOMAS Congress. CIMNE, 2021. http://dx.doi.org/10.23967/wccm-eccomas.2020.211.

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Reports on the topic "Unfitted Finite Elements"

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Martín, A., L. Cirrottola, A. Froehly, R. Rossi, and C. Soriano. D2.2 First release of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.010.

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This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is
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