Codice 36/2012 Titolo On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems Data 2012-09-13 Autore/i Canuto, C.; Verani, M. Link Download full text Pubblicato It will be published on the book in the honor of Enrico Magenes Abstract We provide an overview of the state of the art of adaptive strategies for high-order $hp$ discretizations of partial differential equations; at the same time, we draw attention on some recent results of ours concerning the convergence and complexity analysis of adaptive algorithm of spectral and spectral-element type. Complexity is studied under the assumption that the solution belongs to a sparsity class of exponential type, which means that its best $N$-term approximation error in the chosen piecewise polynomial basis decays at an exponential rate with respect to $N$.