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Numerical analysis of a singularly perturbed convection diffusion problem with shift in space (2207.09218v1)
Published 19 Jul 2022 in math.NA and cs.NA
Abstract: 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.