Conservation of forces and total work at the interface using the internodes method
type: Item
instance of: scholarly article
title: Conservation of forces and total work at the interface using the internodes method
zbMATH Open document ID: 1501.65150
author: Paola Gervasio
author: Simone Deparis
published in: Vietnam Journal of Mathematics
publication date: 2022-10-13T00:00:00Z
review text: This paper focus on the Internodes method, which treats the non-conforming discretizations of partial differential equations in 2D and 3D domains partitioned using disjoint subdomains. In particular, the conservativity of the applied Internodes method is addressed. It is shown that both the total force as well as the total work generated by the numerical solution at the interface vanish for mesh size approaching zero provided that the hp-finite element method is used with the same decay as the error in the H1-broken Sobolev norm. The analysis is performed with the aid of second-order elliptic PDEs. The numerical experiments confirming the theoretical findings are presented for 2D and 3D cases.
reviewed by: Petr Sváček
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 7600695
zbMATH Keywords: domain decomposition
zbMATH Keywords: non-conforming coupling
zbMATH Keywords: conservation properties
zbMATH Keywords: finite element method
zbMATH Keywords: \textit{hp}-finite element method
zbMATH Keywords: spectral element method
MaRDI profile type: Publication
full work available at URL: s10013-022-00560-9
OpenAlex ID: W4280554078
cites work: A finite element method for domain decomposition with non-matching grids
cites work: Non-conforming spectral element-finite element approximations for partial differential equations
cites work: The mortar finite element method with Lagrange multipliers
cites work: Q2771283
cites work: Q3138732
cites work: Q4288485
cites work: Variational discretization of elliptic boundary value problems.
cites work: Conjugate approximation functions in finite-element analysis
cites work: Q4218290
cites work: INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces
cites work: A Rescaled Localized Radial Basis Function Interpolation on Non-Cartesian and Nonconforming Grids
cites work: A Fluid–Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-Conforming Interfaces
cites work: Q1817825
cites work: The INTERNODES method for the treatment of non-conforming multipatch geometries in isogeometric analysis
cites work: Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations
cites work: INTERNODES for Elliptic Problems
cites work: INTERNODES for Heterogeneous Couplings
cites work: The INTERNODES method for non-conforming discretizations of PDEs
cites work: Transfinite mappings and their application to grid generation
cites work: Q4023365
cites work: Radial basis functions for inter-grid interpolation and mesh motion in FSI problems
cites work: Data Oscillation and Convergence of Adaptive FEM
cites work: Q4303980
cites work: Q4254887
cites work: An introduction to Sobolev spaces and interpolation spaces
cites work: Q4825126
cites work: A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
DOI: 10.1007/S10013-022-00560-9
Recommended article: Q3722006
Recommended article: An interplay between the zero-work forces and work
Recommended article: Q3221489
Recommended article: Interface pressure calculation based on conservation of momentum for front capturing methods
Recommended article: The principle of virtual work and its dual for contact problems
Recommended article: Conservation laws for the mass, momentum, and energy on a phase interface for true and excess surface parameters
Recommended article: The variational energy formulation for the integrated force method
Recommended article: Analysis of continuum by the integrated force method
Recommended article: Q4793081
Recommended article: A Kelvin Theorem and Partial Work of Impulsive Forces
description: scientific article; zbMATH DE number 7600695