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  4. Conservation of Forces and Total Work at the Interface Using the Internodes Method
 
research article

Conservation of Forces and Total Work at the Interface Using the Internodes Method

Deparis, Simone
β€’
Gervasio, Paola
May 10, 2022
Vietnam Journal of Mathematics

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes method is conservative across the interface. If hp-fem discretizations are employed, we prove that both the total force and total work generated by the numerical solution at the interface of the decomposition vanish in an optimal way when the mesh size tends to zero, i.e., like π’ͺ(β„Žπ‘), where p is the local polynomial degree and h the mesh-size. This is the same as the error decay in the H1-broken norm. We observe that the conservation properties of a method are intrinsic to the method itself because they depend on the way the interface conditions are enforced rather then on the problem we are called to approximate. For this reason, in this paper, we focus on second-order elliptic PDEs, although we use the terminology (of forces and works) proper of linear elasticity. Two and three dimensional numerical experiments corroborate the theoretical findings, also by comparing Internodes with Mortar and WACA methods.

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Type
research article
DOI
10.1007/s10013-022-00560-9
Author(s)
Deparis, Simone
Gervasio, Paola
Date Issued

2022-05-10

Published in
Vietnam Journal of Mathematics
Subjects

Domain decomposition

β€’

Non-conforming coupling

β€’

Conservation properties

β€’

Finite element method

β€’

hp-finite element method

β€’

Spectral element method

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
SCI-SB-SD  
FunderGrant Number

FNS

200021_197021

Available on Infoscience
May 11, 2022
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/187829
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