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arXiv · 1712.09267

A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square

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

Both practice and analysis of adaptive $p$-FEMs and $hp$-FEMs raise the question what increment in the current polynomial degree $p$ guarantees a $p$-independent reduction of the Galerkin error. We answer this question for the $p$-FEM in the simplified context of homogeneous Dirichlet problems for the Poisson equation in the two dimensional unit square with polynomial data of degree $p$. We show that an increment proportional to $p$ yields a $p$-robust error reduction and provide computational evidence that a constant increment does not.

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Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson, Marco Verani. 2017-12-26. A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square. https://arxiv.org/abs/1712.09267

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