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Multimesh finite element methods: Solving PDEs on multiple intersecting meshes
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 343, p. 672-689Article in journal (Refereed) Published
Abstract [en]

We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper (Johansson et al., 2018), we analyze the proposed method and prove optimal order convergence and stability.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 343, p. 672-689
Keywords [en]
FEM, Unfitted mesh, Non-matching mesh, Multimesh, CutFEM, Nitsche
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-153109DOI: 10.1016/j.cma.2018.09.009ISI: 000447411100029Scopus ID: 2-s2.0-85054002398OAI: oai:DiVA.org:umu-153109DiVA, id: diva2:1262692
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved

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Larson, Mats G.

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