Singularly perturbed reaction-diffusion problems as first order systems

2021/03/19 by Franz, Sebastian
#65N12 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2103.10750

Abstract

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 H²-norm for the second order formulation.

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