On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems

Code:
36/2012
Title:
On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems
Date:
Thursday 13th September 2012
Author(s):
Canuto, C.; Verani, M.
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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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It will be published on the book in the honor of Enrico Magenes