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.
CITATION STYLE
Canuto, C., & Verani, M. (2013). On the numerical analysis of adaptive spectral/hp methods for elliptic problems. In Springer INdAM Series (Vol. 4, pp. 165–192). Springer International Publishing. https://doi.org/10.1007/978-88-470-2592-9_11
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