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

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. Nhumer. 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, Internal. J. Numer. Anal. Modeling 4 (2007) 342-352], applied to the partial differential equation del(2)phi + alpha phi = 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. Theoretical error estimates are illustrated by numerical experiments. (C) 2007 Elsevier B.V. All rights reserved.