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A dissimilar non-matching HDG discretization for Stokes flows

Manríquez, Jaime LU orcid ; Nguyen, Ngoc Cuong and Solano, Manuel (2022) In Computer Methods in Applied Mechanics and Engineering 399.
Abstract

In this work we propose and analyze an HDG method for the Stokes equation whose domain is discretized by two independent polygonal subdomains with different meshsizes. This causes a non-conformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to appropriately couple these two different discretizations, we propose suitable transmission conditions to preserve the high order convergence of the scheme. Furthermore, stability estimates are established in order to show the well-posedness of the method and the error estimates. In particular, for smooth enough solutions, the L2 norm of the errors associated to the approximations of the velocity gradient, the velocity and the pressure... (More)

In this work we propose and analyze an HDG method for the Stokes equation whose domain is discretized by two independent polygonal subdomains with different meshsizes. This causes a non-conformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to appropriately couple these two different discretizations, we propose suitable transmission conditions to preserve the high order convergence of the scheme. Furthermore, stability estimates are established in order to show the well-posedness of the method and the error estimates. In particular, for smooth enough solutions, the L2 norm of the errors associated to the approximations of the velocity gradient, the velocity and the pressure are of order hk+1, where h is the meshsize and k is the polynomial degree of the local approximation spaces. Moreover, the method presents superconvergence of the velocity trace and the divergence-free postprocessed velocity. Finally, we show numerical experiments that validate our theory and the capacities of the method.

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type
Contribution to journal
publication status
published
subject
keywords
Dissimilar meshes, Hybrid method, Non-coincident meshes, Non-matching meshes, Stokes flows
in
Computer Methods in Applied Mechanics and Engineering
volume
399
article number
115292
publisher
Elsevier
external identifiers
  • scopus:85134387832
ISSN
0045-7825
DOI
10.1016/j.cma.2022.115292
language
English
LU publication?
yes
id
4959e61f-5149-4662-957b-43df1ddd57c0
date added to LUP
2022-09-05 14:25:00
date last changed
2024-06-27 20:15:23
@article{4959e61f-5149-4662-957b-43df1ddd57c0,
  abstract     = {{<p>In this work we propose and analyze an HDG method for the Stokes equation whose domain is discretized by two independent polygonal subdomains with different meshsizes. This causes a non-conformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to appropriately couple these two different discretizations, we propose suitable transmission conditions to preserve the high order convergence of the scheme. Furthermore, stability estimates are established in order to show the well-posedness of the method and the error estimates. In particular, for smooth enough solutions, the L<sup>2</sup> norm of the errors associated to the approximations of the velocity gradient, the velocity and the pressure are of order h<sup>k+1</sup>, where h is the meshsize and k is the polynomial degree of the local approximation spaces. Moreover, the method presents superconvergence of the velocity trace and the divergence-free postprocessed velocity. Finally, we show numerical experiments that validate our theory and the capacities of the method.</p>}},
  author       = {{Manríquez, Jaime and Nguyen, Ngoc Cuong and Solano, Manuel}},
  issn         = {{0045-7825}},
  keywords     = {{Dissimilar meshes; Hybrid method; Non-coincident meshes; Non-matching meshes; Stokes flows}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Computer Methods in Applied Mechanics and Engineering}},
  title        = {{A dissimilar non-matching HDG discretization for Stokes flows}},
  url          = {{http://dx.doi.org/10.1016/j.cma.2022.115292}},
  doi          = {{10.1016/j.cma.2022.115292}},
  volume       = {{399}},
  year         = {{2022}},
}