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A hybridizable discontinuous Galerkin method for Stokes/Darcy coupling on dissimilar meshes

Bermúdez, Isaac ; Manríquez, Jaime LU orcid and Solano, Manuel (2025) In IMA Journal of Numerical Analysis
Abstract

We present and analyze a hybridizable discontinuous Galerkin method for coupling Stokes and Darcy equations, whose domains are discretized by two independent triangulations. This causes nonconformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to properly couple the two different discretizations and obtain a high-order scheme, we propose suitable transmission conditions based on mass conservation, equilibrium of normal forces and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide, we use the Transfer Path Method to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the nonconformity and the gap are... (More)

We present and analyze a hybridizable discontinuous Galerkin method for coupling Stokes and Darcy equations, whose domains are discretized by two independent triangulations. This causes nonconformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to properly couple the two different discretizations and obtain a high-order scheme, we propose suitable transmission conditions based on mass conservation, equilibrium of normal forces and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide, we use the Transfer Path Method to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the nonconformity and the gap are explicit in the constants. Finally, numerical experiments that illustrate the performance of the method are shown.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
discontinuous Galerkin, dissimilar meshes, hybrid method, nonmatching meshes, Stokes/Darcy, Transfer Path Method
in
IMA Journal of Numerical Analysis
article number
drae109
pages
36 pages
publisher
Oxford University Press
external identifiers
  • scopus:105018124189
ISSN
0272-4979
DOI
10.1093/imanum/drae109
language
English
LU publication?
yes
additional info
Publisher Copyright: © The Author(s) 2025. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
id
1ebb0479-8f81-4d4b-bc53-783a950a7ec1
date added to LUP
2025-10-30 08:24:13
date last changed
2025-11-13 11:39:09
@article{1ebb0479-8f81-4d4b-bc53-783a950a7ec1,
  abstract     = {{<p>We present and analyze a hybridizable discontinuous Galerkin method for coupling Stokes and Darcy equations, whose domains are discretized by two independent triangulations. This causes nonconformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to properly couple the two different discretizations and obtain a high-order scheme, we propose suitable transmission conditions based on mass conservation, equilibrium of normal forces and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide, we use the Transfer Path Method to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the nonconformity and the gap are explicit in the constants. Finally, numerical experiments that illustrate the performance of the method are shown.</p>}},
  author       = {{Bermúdez, Isaac and Manríquez, Jaime and Solano, Manuel}},
  issn         = {{0272-4979}},
  keywords     = {{discontinuous Galerkin; dissimilar meshes; hybrid method; nonmatching meshes; Stokes/Darcy; Transfer Path Method}},
  language     = {{eng}},
  month        = {{04}},
  publisher    = {{Oxford University Press}},
  series       = {{IMA Journal of Numerical Analysis}},
  title        = {{A hybridizable discontinuous Galerkin method for Stokes/Darcy coupling on dissimilar meshes}},
  url          = {{http://dx.doi.org/10.1093/imanum/drae109}},
  doi          = {{10.1093/imanum/drae109}},
  year         = {{2025}},
}