Relevant bibliographies by topics / Unfitted mesh methods

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Academic literature on the topic 'Unfitted mesh methods'

Author: Grafiati
Published: 5 October 2024
Last updated: 31 July 2025

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Journal articles on the topic "Unfitted mesh methods"

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Fernández, Miguel A., and Mikel Landajuela. "Splitting schemes and unfitted-mesh methods for the coupling of an incompressible fluid with a thin-walled structure." IMA Journal of Numerical Analysis 40, no. 2 (2019): 1407–53. http://dx.doi.org/10.1093/imanum/dry098.

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Abstract Two unfitted-mesh methods for a linear incompressible fluid/thin-walled structure interaction problem are introduced and analyzed. The spatial discretization is based on different variants of Nitsche’s method with cut elements. The degree of fluid–solid splitting (semi-implicit or explicit) is given by the order in which the space and time discretizations are performed. The a priori stability and error analysis shows that strong coupling is avoided without compromising stability and accuracy. Numerical experiments with a benchmark illustrate the accuracy of the different methods propo
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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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Heimann, Fabian, Christoph Lehrenfeld, Paul Stocker, and Henry von Wahl. "Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems." ESAIM: Mathematical Modelling and Numerical Analysis, August 1, 2023. http://dx.doi.org/10.1051/m2an/2023064.

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We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedom in discontinuous Galerkin methods, thereby, the costs for solving arising linear systems significantly. This work shows that they are also an excellent way to reduce the number of degrees of freedom in an unfitted setting. We present a unified analysis of a class of geometrically unfitted discontinuous Galerkin methods with different stabilisation mechanisms to deal with small cuts between the geometry and the mesh
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Frachon, Thomas, Erik Nilsson, and Sara Zahedi. "Divergence-free cut finite element methods for Stokes flow." BIT Numerical Mathematics 64, no. 4 (2024). http://dx.doi.org/10.1007/s10543-024-01040-x.

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AbstractWe develop two unfitted finite element methods for the Stokes equations based on $$\textbf{H}^{{{\,\textrm{div}\,}}}$$ H div -conforming finite elements. Both cut finite element methods exhibit optimal convergence order for the velocity, pointwise divergence-free velocity fields, and well-posed linear systems, independently of the position of the boundary relative to the computational mesh. The first method is a cut finite element discretization of the Stokes equations based on the Brezzi–Douglas–Marini (BDM) elements and involves interior penalty terms to enforce tangential continuity
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Heimann, Fabian, and Christoph Lehrenfeld. "Geometry error analysis of a parametric mapping for higher order unfitted space–time methods." IMA Journal of Numerical Analysis, March 10, 2025. https://doi.org/10.1093/imanum/drae098.

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Abstract In Heimann, Lehrenfeld, and Preuß (2023, SIAM J. Sci. Comp., 45(2), B139–B165), new geometrically unfitted space–time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For geometrically higher-order accuracy a parametric mapping on a background space–time tensor-product mesh has been used. In this paper, we concentrate on the geometrical accuracy of the approximation and derive rigorous bounds for the distance between the realized and an ideal mapping in different norms and derive results
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Jankuhn, Thomas, Maxim A. Olshanskii, Arnold Reusken, and Alexander Zhiliakov. "Error analysis of higher order trace finite element methods for the surface Stokes equation." Journal of Numerical Mathematics, October 4, 2020. http://dx.doi.org/10.1515/jnma-2020-0017.

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AbstractThe paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.
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Pretti, Giuliano, Robert E. Bird, Nathan D. Gavin, William M. Coombs, and Charles E. Augarde. "A Stable Poro‐Mechanical Formulation for Material Point Methods Leveraging Overlapping Meshes and Multi‐Field Ghost Penalisation." International Journal for Numerical Methods in Engineering 126, no. 5 (2025). https://doi.org/10.1002/nme.7630.

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ABSTRACTThe Material Point Method (MPM) is widely used to analyse coupled (solid‐water) problems under large deformations/displacements. However, if not addressed carefully, MPM u‐p formulations for poromechanics can be affected by two major sources of instability. Firstly, inf‐sup condition violation can arise when the spaces for the displacement and pressure fields are not chosen correctly, resulting in an unstable pressure field when the equations are monolithically solved. Secondly, the intrinsic nature of particle‐based discretisation makes the MPM an unfitted mesh‐based method, which can
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Kirchhart, Matthias. "On particles and splines in bounded domains." ESAIM: Mathematical Modelling and Numerical Analysis, May 6, 2020. http://dx.doi.org/10.1051/m2an/2020032.

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We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain's boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in $W^{s,p}$-norms, $s\in\mathbb{R}$, $1\leq p\leq\infty$.
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9

Yang, Fanyi. "The least squares finite element method for elasticity interface problem on unfitted mesh." ESAIM: Mathematical Modelling and Numerical Analysis, March 7, 2024. http://dx.doi.org/10.1051/m2an/2024015.

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In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal, and the exact solution $(\bsigma, \bu)$ belongs to $H^s(\div; \Omega_0 \cup \Omega_1) \times H^{1+s}(\Omega_0 \cup \Omega_1)$ with $s > 1/2$. Two types of least squares functionals are defined to seek the numerical solution. The first is defined by simply applying the $L^2$ norm least squares principle, and requires the condition $s \geq 1$. The second i
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Lehrenfeld, Christoph, Tim van Beeck, and Igor Voulis. "Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem." Mathematics of Computation, October 30, 2024. http://dx.doi.org/10.1090/mcom/4027.

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In this paper we present a new H ( div ) H(\operatorname {div}) -conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is to formulate the divergence-constraint on the active mesh, instead of the physical domain, in order to obtain robustness with respect to cut configurations without the need for a stabilization that pollutes the mass balance. This change in the formulation results in a slight inconsistency, but does not affect the accuracy of the flu
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Dissertations / Theses on the topic "Unfitted mesh methods"

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Landajuela, Larma Mikel. "Coupling schemes and unfitted mesh methods for fluid-structure interaction." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066053/document.

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Cette thèse est dédiée à la simulation numérique des systèmes mécaniques impliquant l'interaction entre une structure mince déformable et un fluide incompressible interne ou qui l'entoure.Dans la première partie, nous introduisons deux nouvelles classes de schémas de couplage explicites en utilisant des maillages compatibles. Les méthodes proposées combinent une certaine consistance Robin dans le système avec (i) un schéma à pas fractionnaire pour le fluide ou (ii) une discrétisation temporelle d'ordre deux pour le fluide et le solide. Les propriétés de stabilité des méthodes sont analysées da
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Corti, Daniele Carlo. "Numerical methods for immersed fluid-structure interaction with enhanced interfacial mass conservation." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS176.

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Cette thèse porte sur la modélisation, l'analyse numérique et à la simulation de problèmes d'interaction fluide-structure pour des structures minces immergées dans un fluide visqueux incompressible. La motivation sous-jacente de ce travail est la simulation des phénomènes d'interaction fluide-structure impliqués dans la simulation des valves cardiaques. Du point de vue méthodologique, un accent particulier est mis sur des méthodes avec maillage non conformes qui permettent de garantir la précision du résultat en minimisant le coût computationnel. Un aspect essentiel est de garantir la conserva
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Reports on the topic "Unfitted mesh methods"

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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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