A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
| Authors |
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|---|---|
| Publication date | 2019 |
| Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
| Volume | Issue number | 53 | 3 |
| Pages (from-to) | 987-1003 |
| Organisations |
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| Abstract | Both practice and analysis of p-FEMs and adaptive 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. |
| Document type | Article |
| Language | English |
| Published at |
https://doi.org/10.1051/m2an/2019015
(Final published version)
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| Published at |
https://arxiv.org/abs/1712.09267
(Submitted manuscript)
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| Other links | |
| Downloads |
A saturation property for the spectral-Galerkin subm. vers
(Submitted manuscript)
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