Year: 2017
Author: Serge Nicaise, Christos Xenophontos
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 2 : pp. 152–168
Abstract
We perform the analysis of the $hp$ finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust exponential convergence, as the degree $p$ of the approximating polynomials is increased, when the error is measured in the energy norm associated with the boundary value problem. In the present article we sharpen the result by showing that the $hp$-Finite Element Method (FEM) on Spectral Boundary Layer Meshes leads to robust exponential convergence in a stronger, more balanced norm. Several numerical results illustrating and extending the theory are also presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1607-m2014-0187
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 2 : pp. 152–168
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Singularly perturbed transmission problem Boundary layers Interface layers $hp$-FEM Balanced norm Exponential convergence.