%0 Journal Article %T Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations %A JongKyum Kwon %A Soorok Ryu %A Philsu Kim %A Sang Dong Kim %J Journal of Applied Mathematics %D 2012 %I Hindawi Publishing Corporation %R 10.1155/2012/245051 %X The uniform bounds on eigenvalues of ªâ£¿£¿12ªâ2 are shown both analytically and numerically by the 1 finite element preconditioner ªâ£¿£¿12 for the Legendre spectral element system ªâ2= which is arisen from a coupled elliptic system occurred by an optimal control problem. The finite element preconditioner is corresponding to a leading part of the coupled elliptic system. %U http://www.hindawi.com/journals/jam/2012/245051/