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arXiv · 1511.00233

Adaptive Spectral Galerkin Methods with Dynamic Marking

Claudio Canuto·Ricardo H. Nochetto·Rob Stevenson·Marco Verani
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Abstract

The convergence and optimality theory of adaptive Galerkin methods is almost exclusively based on the D\"orfler marking. This entails a fixed parameter and leads to a contraction constant bounded below away from zero. For spectral Galerkin methods this is a severe limitation which affects performance. We present a dynamic marking strategy that allows for a super-linear relation between consecutive discretization errors, and show exponential convergence with linear computational complexity whenever the solution belongs to a Gevrey approximation class.

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Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson, Marco Verani. 2015-11-01. Adaptive Spectral Galerkin Methods with Dynamic Marking. https://arxiv.org/abs/1511.00233

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