An \(hp\) finite element method for \(4^{\mathrm{th}}\) order singularly perturbed problems

DOI10.1007/s11075-016-0108-9zbMath1360.65201OpenAlexW2291244043MaRDI QIDQ329329

Philippos Constantinou, Charalambia Varnava, Christos Xenophontos

Publication date: 21 October 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0108-9

zbMATH Keywords

numerical experimentsboundary layersexponential convergence\(hp\)-finite element methodbalanced normspectral boundary layer mesh\(4^-{\mathrm{th}}\) order singularly perturbed problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (8)

On the finite element approximation of fourth-order singularly perturbed eigenvalue problems ⋮ An \(hp\) finite element method for \(4^{\mathrm{th}}\) order singularly perturbed problems ⋮ An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions ⋮ Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE ⋮ A parameter robust finite element method for fourth order singularly perturbed problems ⋮ Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions ⋮ A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains ⋮ Numerical treatment of singularly perturbed fourth-order two-parameter problems

Cites Work

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• Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations
• A \(C^{1}\)-conforming \(hp\) finite element method for fourth order singularly perturbed boundary value problems
• An \(hp\) finite element method for \(4^{\mathrm{th}}\) order singularly perturbed problems
• Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales
• Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
• 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
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
• Robust exponential convergence of hp FEM for singularly perturbed reaction-diffusion systems with multiple scales

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