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Multimesh finite element methods: Solving PDEs on multiple intersecting meshes

Journal article
Authors A. Johansson
B. Kehlet
M. G. Larson
Anders Logg
Published in Computer Methods in Applied Mechanics and Engineering
Volume 343
Pages 672-689
ISSN 0045-7825
Publication year 2019
Published at Department of Mathematical Sciences
Pages 672-689
Language en
Keywords FEM, Unfitted mesh, Non-matching mesh, Multimesh, CutFEM, Nitsche, solid mechanics, nitsches method, cell method, discontinuous galerkin, domain decomposition, overlapping grids, integration, refinement, elasticity, boundary, Engineering, Mathematics, Mechanics
Subject categories Mathematics


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. (C) 2018 Elsevier B.V. All rights reserved.

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