On the $p$-version of FEM in one dimension: The known and unknown features
Numerical Analysis
2014-01-08 v1
Abstract
The paper analyses the convergence of the -version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element and there is a Gibbs phenomenon in the neighborhood of the point where the solution is not analytic. The major result is a conjecture written in the form of a theorem. The conjecture is based on careful numerical computations. The known theoretical results are stated.
Keywords
Cite
@article{arxiv.1401.1483,
title = {On the $p$-version of FEM in one dimension: The known and unknown features},
author = {Ivo Babuška and Harri Hakula},
journal= {arXiv preprint arXiv:1401.1483},
year = {2014}
}