[Zurück]

J. Melenk, C. Xenophontos:
"Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion equations";
in: "ASC Report 24/2014", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, S. 1 - 24.

The hp-version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed in one- and two-dimensional domains with analytic boundary. On suitably designed Spectral Boundary Layer meshes, robust exponential convergence in a balanced norm is shown. This balanced norm is stronger than the en-
ergy norm in that the boundary layers are O(1) uniformly in the singular perturbation parameter. Robust exponential convergence in the maximum norm is also established. The theoretical findings are illustrated with two numerical experiments.

http://www.asc.tuwien.ac.at/preprint/2014/asc24x2014.pdf