We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and Hdiv-conforming elements for the second component we provide a convergence analysis on layer adapted meshes and an optimal convergence order in a balanced norm that is comparable with a balanced H2-norm for the second order formulation.
@article{arxiv.2103.10750,
title = {Singularly perturbed reaction-diffusion problems as first order systems},
author = {Sebastian Franz},
journal= {arXiv preprint arXiv:2103.10750},
year = {2021}
}