Condition number and diagonal preconditioning: Comparison of the \(p\)-version and the spectral element methods
For adaptive schemes the hierarchical basis is used in the \(p\)-version of the finite element method. The condition number for the matrices of the commonly used basis introduced by \textit{I. Babuška} and \textit{B. A. Szabo} [Finite element analysis (1991; Zbl 0792.73003)] is investigated. For \(d\)-dimensional rectangular elements it is shown that the condition number is equivalent to \(p^{4(d-1)}\) and to \(p^{4d}\) for the stiffness and the mass matrix. Moreover, the usual diagonal preconditioning divides in the previous orders the exponents of \(p\) by two. The results are compared to those obtained for spectral elements.
scientific article; zbMATH DE number 932009