Robust Hybrid Finite Element Methods for Singularly Perturbed Reaction-Diffusion Problems

The authors propose and analyze primal and dual hybrid finite element methods for a singularly perturbed reaction-diffusion problem. The methods achieve uniform robustness with respect to the singular perturbation parameter by enriching the local discretization spaces with modified face bubble functions that decay exponentially in the interior of elements depending on the ratio of the perturbation parameter and the local mesh-size.