A. Quarteroni and E. Zampieri, “Finite Element Preconditioning for Legendre Spectral Collocation Approximations to Elliptic Equations and Systems,” SIAM Journal on Numerical Analysis, Vol. 29, No. 4, 1992, pp. 917-936. doi:10.1137/0729056

has been cited by the following article:

• TITLE: Finite Difference Preconditioners for Legendre Based Spectral Element Methods on Elliptic Boundary Value Problems

  AUTHORS: Seonhee Kim, Amik St-Cyr, Sang Dong Kim

  KEYWORDS: Finite Difference Preconditioner; Iterative Method; Spectral Element Method; Elliptic Operator

  JOURNAL NAME: Applied Mathematics, Vol.4 No.5, May 22, 2013

  ABSTRACT: Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.