Numerical analysis of a singularly perturbed convection diffusion problem with shift in space

07/19/2022

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by   Mirjana Brdar, et al.

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We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high order finite element method on layer adapted meshes. We also apply a new idea of using a coarser mesh in places where weak layers appear. Numerical experiments confirm our theoretical results.