Contributions to Books:

M. Faustmann, J. Melenk:
"Robust exponential convergence of $hp$-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains";
in: "ASC Report 25/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 17.

English abstract:
The hp-version of the finite element method is applied to singularly perturbed reaction-diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitable refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.

high order FEM, singular perturbation, balanced norm, uniform estimates

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.