Finite element preconditioning on spectral element discretizations for coupled elliptic equations (Q410899)

Summary: The uniform bounds on eigenvalues of \(\hat{B}^{-1}_{h^2} \hat{A}_{N^2}\) are shown both analytically and numerically by the \(\mathcal P_{1}\) finite element preconditioner \(\hat{B}^{-1}_{h^2}\) for the Legendre spectral element system \(\hat A_{N^2} \mathbf{\underline{u} = \underline{f}}\) 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.