An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions

DOI10.1016/j.camwa.2017.02.009zbMath1397.65257OpenAlexW2589587600MaRDI QIDQ1663819

Christos Xenophontos, Philippos Constantinou

Publication date: 24 August 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.02.009

zbMATH Keywords

boundary layers\(hp\) finite element methodfourth-order singularly perturbed problemrobust exponential convergence

Mathematics Subject Classification ID

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 (5)

An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions ⋮ Solving a singular beam equation by the method of energy boundary functions ⋮ The Bogner-Fox-Schmit element finite volume methods on the Shishkin mesh for fourth-order singularly perturbed elliptic problems ⋮ Local discontinuous Galerkin method for a singularly perturbed fourth-order problem of reaction-diffusion type ⋮ Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions

Cites Work

• 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
• An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions
• Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems
• On the Finite Element Approximation of Systems of Singularly Perturbed Rection-diffusion Equations
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• The Approximation Theory for thep-Version of the Finite Element Method
• The p-Version of the Finite Element Method for Problems Requiring $C^1$-Continuity
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• On the Stability and Convergence of Higher-Order Mixed Finite Element Methods for Second-Order Elliptic Problems
• Thehp finite element method for singularly perturbed problems in nonsmooth domains
• MIXED hp-FEM ON ANISOTROPIC MESHES
• Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• Robust exponential convergence of hp FEM for singularly perturbed reaction-diffusion systems with multiple scales
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions