Skip to Main content Skip to Navigation
Journal articles

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

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.
Document type :
Journal articles
Complete list of metadata

https://hal-uphf.archives-ouvertes.fr/hal-03212509
Contributor : Mélissa Defond Connect in order to contact the contributor
Submitted on : Thursday, April 29, 2021 - 4:31:05 PM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

Identifiers

Collections

Citation

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

Share

Metrics

Record views

30