Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Journal articles
  4. Geometric transformation of finite element methods: Theory and applications
 
Loading...
Thumbnail Image
research article

Geometric transformation of finite element methods: Theory and applications

Holst, Michael
•
Licht, Martin  
October 1, 2023
Applied Numerical Mathematics

We present a new analysis of finite element methods for partial differential equations over curved domains. In many applications, a change of variables translates a physical Poisson problem over a curved physical domain into a parametric Poisson problem over a polytopal parametric domain. Whilst this change of variables greatly simplifies the geometry and numerical implementations, the coordinate transformation typically features only low regularity. In the parametric Poisson problem, this manifests as rough coefficients and data, which diminish the elliptic regularity, and as roughness of the parametric solution. Our main result addresses how to nevertheless recover high-order finite element convergence rates, the key component being a recently developed broken Bramble-Hilbert lemma. This analysis has numerous applications, where the geometric transformation is either computable or merely a theoretical tool. We propose a simplified technique as easier, more broadly applicable, yet just as powerful as previous isoparametric methods. In particular, we reassess the error analysis of isoparametric finite element methods and prove high-order error estimates for isoparametric FEM even when the physical solution is not continuous. Numerical examples confirm our theoretical predictions.& COPY; 2023 The Authors. Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY license (http://creativecommons.org/licenses /by /4 .0/).

  • Details
  • Metrics
Type
research article
DOI
10.1016/j.apnum.2023.07.002
Web of Science ID

WOS:001045879300001

Author(s)
Holst, Michael
•
Licht, Martin  
Date Issued

2023-10-01

Published in
Applied Numerical Mathematics
Volume

192

Start page

389

End page

413

Subjects

Mathematics, Applied

•

Mathematics

•

a priori error estimates

•

finite element method

•

piecewise bramble-hilbert lemma

•

numerical-analysis

•

elliptic pdes

•

interpolation

•

domains

•

approximation

•

equations

•

nurbs

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
MATH  
Available on Infoscience
August 28, 2023
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/200108
Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés