Codice | 02/2018 |
Titolo | A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square |
Data | 2018-01-03 |
Autore/i | Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M. |
Link | Download full text |
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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