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Volume 4, Issue 3-4
A Least-Squares Method for Consistent Mesh Tying

P. Bochev & D. Day

Int. J. Numer. Anal. Mod., 4 (2007), pp. 342-352.

Published online: 2007-04

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  • Abstract

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.

  • Keywords

finite elements, mesh tying, least-squares, first-order elliptic systems.

  • AMS Subject Headings

65F10, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-342, author = {P. Bochev and D. Day}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/865.html} }
TY - JOUR T1 - A Least-Squares Method for Consistent Mesh Tying AU - P. Bochev & D. Day JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 342 EP - 352 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/865.html KW - finite elements, mesh tying, least-squares, first-order elliptic systems. AB -

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. Bochev and D. Day. (2007). A Least-Squares Method for Consistent Mesh Tying. International Journal of Numerical Analysis and Modeling. 4 (3-4). 342-352. doi:
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