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MultiMesh Finite Element Methods: Solving PDEs on Multiple Intersecting Meshes

Abstract

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.
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Category

Academic article

Language

English

Author(s)

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics
  • Chalmers University of Technology
  • Umeå University
  • Simula Research Laboratory

Year

2019

Published in

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

Volume

343

Issue

1

Page(s)

672 - 689

View this publication at Norwegian Research Information Repository