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Journal Articles Computational Methods in Applied Mathematics Year : 2013

Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method

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Xenophontos Christos
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Abstract

Abstract. We consider the finite element approximation of the solution to a singularly perturbed second order differential equation with a constant delay. The boundary value problem can be cast as a singularly perturbed transmission problem, whose solution may be decomposed into a smooth part, a boundary layer part, an interior/interface layer part and a remainder. Upon discussing the regularity of each component, we show that under the assumption of analytic input data, the hp version of the finite element method on an appropriately designed mesh yields robust exponential convergence rates. Numerical results illustrating the theory are also included.
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Dates and versions

hal-03212509 , version 1 (29-04-2021)

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Serge Nicaise, Xenophontos Christos. Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method. Computational Methods in Applied Mathematics, 2013, 13 (1), pp.21-37. ⟨10.1515/cmam-2012-0001⟩. ⟨hal-03212509⟩
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