Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

Abstract

The uniform bounds on eigenvalues of B^h2−1A^N2 are shown both analytically and numerically by the P1 finite element preconditioner B^h2−1 for the Legendre spectral element system A^N2u¯=f¯ 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.