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Title: L2-projected least-squares finite element methods for the Stokes equations
Authors: Duan, H.-Y. 
Lin, P. 
Saikrishnan, P.
Tan, R.C.E. 
Keywords: L2 projection
The Stokes equation
Velocity-pressure-vorticity least-squares finite element method
Issue Date: 2006
Citation: Duan, H.-Y., Lin, P., Saikrishnan, P., Tan, R.C.E. (2006). L2-projected least-squares finite element methods for the Stokes equations. SIAM Journal on Numerical Analysis 44 (2) : 732-752. ScholarBank@NUS Repository.
Abstract: Two new L2 least-squares (LS) finite element methods are developed for the velocity-pressure-vorticity first-order system of the Stokes problem with Dirichlet velocity boundary condition, A key feature of these new methods is that a local or almost local L2 projector is applied to the residual of the momentum equation. Such L2 projection is always defined onto the linear finite element space, no matter which finite element spaces are used for velocity-pressure-vorticity variables. Consequently, the implementation of this L2-projected LS method is almost as easy as that of the standard L2 LS method. More importantly, the former has optimal error estimates in L2-norm, with respect to both the order of approximation and the required regularity of the exact solution for velocity using equal-order interpolations and for all three variables (velocity, pressure, and vorticity) using unequal-order interpolations. Numerical experiments are given to demonstrate the theoretical results. © 2006 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Numerical Analysis
ISSN: 00361429
DOI: 10.1137/040613573
Appears in Collections:Staff Publications

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