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Title: Analysis of a least-squares finite element method for the thin plate problem
Authors: Duan, H.-y. 
Gao, S.-q.
Jiang, B.-n.
Tan, R.C.E. 
Keywords: Deflection-slope-moment-shear force
Least-squares finite element method
Thin plate equation
Issue Date: May-2009
Citation: Duan, H.-y., Gao, S.-q., Jiang, B.-n., Tan, R.C.E. (2009-05). Analysis of a least-squares finite element method for the thin plate problem. Applied Numerical Mathematics 59 (5) : 976-987. ScholarBank@NUS Repository.
Abstract: A new least-squares finite element method is analyzed for the thin plate problem subject to various boundary conditions (clamped, simply supported and free). The unknown variables are deflection, slope, moment and shear force. The coercivity property is established. As a result, all variables can be approximated by any conforming finite elements. In particular, an H1-ellipticity is proven for the free thin plate. This indicates that optimal error bounds hold for all variables with the use of equal-order continuous elements. Numerical experiments are performed to confirm the theoretical results obtained. © 2008 IMACS.
Source Title: Applied Numerical Mathematics
ISSN: 01689274
DOI: 10.1016/j.apnum.2008.03.041
Appears in Collections:Staff Publications

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