Archivio Istituzionale della RicercaWe 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.
On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems / Canuto, Claudio; Marco, Verani - In: Springer INdAM Series - Analysis and Numerics of Partial Differential Equations / F. Brezzi, P. Colli Franzone, U. Gianazza, G. Gilardi. - STAMPA. - Milano : Springer Verlag, 2013. - ISBN 9788847025912. - pp. 165-192 [10.1007/978-88-470-2592-9_11]
On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems
CANUTO, CLAUDIO;
2013
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.
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https://hdl.handle.net/11583/2506049
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