Analysis and computation of a leastsquares method for consistent mesh tying
Abstract
We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a firstorder patch test [T.A. Laursen, M.W. Heinstein, Consistent meshtying methods for topologically distinct discretized surfaces in nonlinear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a leastsquares method for mesh tying [P. Bochev, D.M. Day, A leastsquares method for consistent mesh tying, Internat. J. Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation ∇^{2}φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the leastsquares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Computational Mathematics and Algorithms
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1426952
 Report Number(s):
 SAND20071510J
Journal ID: ISSN 03770427; 526844
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational and Applied Mathematics
 Additional Journal Information:
 Journal Volume: 218; Journal Issue: 1; Journal ID: ISSN 03770427
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Finite elements; Mesh tying; Leastsquares; Firstorder elliptic systems
Citation Formats
Day, David, and Bochev, Pavel. Analysis and computation of a leastsquares method for consistent mesh tying. United States: N. p., 2007.
Web. https://doi.org/10.1016/j.cam.2007.04.049.
Day, David, & Bochev, Pavel. Analysis and computation of a leastsquares method for consistent mesh tying. United States. https://doi.org/10.1016/j.cam.2007.04.049
Day, David, and Bochev, Pavel. Tue .
"Analysis and computation of a leastsquares method for consistent mesh tying". United States. https://doi.org/10.1016/j.cam.2007.04.049. https://www.osti.gov/servlets/purl/1426952.
@article{osti_1426952,
title = {Analysis and computation of a leastsquares method for consistent mesh tying},
author = {Day, David and Bochev, Pavel},
abstractNote = {We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a firstorder patch test [T.A. Laursen, M.W. Heinstein, Consistent meshtying methods for topologically distinct discretized surfaces in nonlinear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a leastsquares method for mesh tying [P. Bochev, D.M. Day, A leastsquares method for consistent mesh tying, Internat. J. Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation ∇2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the leastsquares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.},
doi = {10.1016/j.cam.2007.04.049},
journal = {Journal of Computational and Applied Mathematics},
number = 1,
volume = 218,
place = {United States},
year = {2007},
month = {7}
}
Web of Science
Works referencing / citing this record:
A Nitschebased cut finite element method for a fluidstructure interaction problem
journal, January 2015
 Massing, André; Larson, Mats; Logg, Anders
 Communications in Applied Mathematics and Computational Science, Vol. 10, Issue 2
A Nitschebased cut finite element method for a fluidstructure interaction problem
journal, January 2015
 Massing, André; Larson, Mats; Logg, Anders
 Communications in Applied Mathematics and Computational Science, Vol. 10, Issue 2