Analysis and computation of a least-squares method for consistent mesh tying

Day, David; Bochev, Pavel

doi:10.1016/j.cam.2007.04.049

Analysis and computation of a least-squares method for consistent mesh tying

Journal Article · Tue Jul 10 00:00:00 EDT 2007 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2007.04.049· OSTI ID:1426952

Day, David ^[1]; Bochev, Pavel ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics and Algorithms

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 first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares 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 least-squares 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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1426952

Report Number(s):: SAND--2007-1510J; 526844

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: 1 Vol. 218; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Finite elements
First-order elliptic systems
Least-squares
Mesh tying

Analysis and computation of a least-squares method for consistent mesh tying

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References (17)

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