Singularly Perturbed Reaction–Diffusion Problems as First order systems

Abstract We consider a singularly perturbed reaction diffusion problem as first order two-by-two system. Using piecewise discontinuous polynomials for the component and $$H_{{{\,\mathrm{{div}}\,}}}$$ Hdiv -conforming elements second we provide convergence analysis on layer adapted meshes an optimal in balanced norm that is comparable with $$H^2$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">H2 -norm formulation.