Publication Results

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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