Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains

DOI10.1002/num.21793zbMath1280.65117arXiv1104.0766OpenAlexW2119360422MaRDI QIDQ2864607

Serge Nicaise, Christos Xenophontos

Publication date: 26 November 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.0766

zbMATH Keywords

numerical resultssingular perturbationboundary layersexponential convergencetransmission problems\(hp\) finite element methodsmooth domainsinterface layer

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (1)

Robust coupling of DPG and BEM for a singularly perturbed transmission problem

Cites Work

• \(hp\)-finite element methods for singular perturbations
• hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
• Analytic Regularity for a Singularly Perturbed Problem
• On the robust exponential convergence of hp finite element methods for problems with boundary layers
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• Asymptotic Analysis of the Boundary Layer for the Reissner–Mindlin Plate Model
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