Singularly perturbed reaction-diffusion problems as first order systems

03/19/2021

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by   Sebastian Franz, et al.

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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 H_div-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 H^2-norm for the second order formulation.