Publication Results



Code: 02/2018
Title: A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
Date: Wednesday 3rd January 2018
Author(s) : Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M.
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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.