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EnglishWe 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 / Claudio Canuto; Marco Verani. - STAMPA. - 4(2013), pp. 165-192. [10.1007/978-88-470-2592-9_11]
| Titolo: | On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems | |
| Autori: | ||
| Data di pubblicazione: | 2013 | |
| Titolo del libro: | Springer INdAM Series - Analysis and Numerics of Partial Differential Equations | |
| Abstract: | We provide an overview of the state of the art of adaptive strategies for high-order hp discretiz...ations 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. | |
| ISBN: | 9788847025912 9788847025929 | |
| Appare nelle tipologie: | 2.1 Contributo in volume (Capitolo o Saggio) |
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