@Article{IJNAM-4-3-4,
author = {},
title = {A Least-Squares Method for Consistent Mesh Tying},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2007},
volume = {4},
number = {3-4},
pages = {342--352},
abstract = {<p style="text-align: justify;">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 [12]. A
least-squares method is presented here for mesh tying in the presence of
gaps and overlaps. The least-squares formulation for transmission
problems [5] is extended to settings where subdomain boundaries are not
spatially coincident. The new method is consistent in the sense that it
recovers exactly global polynomial solutions that are in the finite
element space. As a result, the least-squares mesh tying method passes a
patch test of the order of the finite element space by construction.
This attractive computational property is illustrated by numerical
experiments.</p>},
issn = {2617-8710},
doi = {https://doi.org/2007-IJNAM-865},
url = {https://global-sci.com/article/83772/a-least-squares-method-for-consistent-mesh-tying}
}