Robust Hybrid Finite Element Methods for Reaction-Dominated Diffusion Problems
Abstract
For a reaction-dominated diffusion problem we study a primal and a dual hybrid finite element method where weak continuity conditions are enforced by Lagrange multipliers. Uniform robustness of the discrete methods is achieved by enriching the local discretization spaces with modified face bubble functions which decay exponentially in the interior of an element depending on the ratio of the singular perturbation parameter and the local mesh-size. A posteriori error estimators are derived using Fortin operators. They are robust with respect to the singular perturbation parameter. Numerical experiments are presented that show that oscillations, if present, are significantly smaller than those observed in common finite element methods.
Fields of Study & Subjects
Soil
Finite Element Methods
Advanced Numerical Methods in Computational Mathematics
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 4
- Pages
- 1925–1954
- Publication date
- 5 May 2026
- Language
- EN