About the conditioning of matrices in the p-version of the finite element method for second order elliptic problems

In the framework of adaptive methods, bases of hierarchical type are used in the p-version of the finite element method. We have studied the matrices corresponding to the most used basis, introduced by Babuška and Szabo, in the case of d-dimensional rectangular elements. e internal nodes, we show that the condition number is O(p4(d−1)) (resp. O(p4d)) for the stiffness (resp. mass) matrix. er, we show that the usual diagonal preconditioning divides the exponents by two.