Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems

DOI10.1002/num.21723zbMath1307.65170arXiv1101.1218OpenAlexW2133473763MaRDI QIDQ4929252

YongKe Wu, Xiaoping Xie, Li Wang

Publication date: 13 June 2013

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

Full work available at URL: https://arxiv.org/abs/1101.1218

zbMATH Keywords

stabilityconvergencesingular perturbationfinite element methodnumerical experimentfourth-order elliptic problemsrectangular Morley element

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Boundary value problems for higher-order elliptic equations (35J40) 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 (19)

Robust nonconforming polynomial finite elements over quadrilaterals ⋮ Hybrid high-order method for singularly perturbed fourth-order problems on curved domains ⋮ Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem ⋮ Two robust nonconforming \(H^2\)-elements for linear strain gradient elasticity ⋮ Quasi‐uniform convergence analysis of a modified penalty finite element method for nonlinear singularly perturbed bi‐wave problem ⋮ The virtual element method with interior penalty for the fourth-order singular perturbation problem ⋮ An asymptotic-preserving finite element method for a forth order singular perturbation problem with boundary layers ⋮ Superconvergence error analysis of Ciarlet-Raviart mixed finite element method for damped Boussinesq equation ⋮ Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators. ⋮ AC⁰-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem ⋮ Quasi-uniform convergence analysis of rectangular Morley element for the singularly perturbed bi-wave equation ⋮ A Family of Nonconforming Rectangular Elements for Strain Gradient Elasticity ⋮ The nonconforming virtual element method for fourth-order singular perturbation problem ⋮ Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions ⋮ A Morley-Wang-Xu element method for a fourth order elliptic singular perturbation problem ⋮ On a Type of Nonconforming Morley Rectangular Finite Element ⋮ Uniformly convergent C⁰‐nonconforming triangular prism element for fourth‐order elliptic singular perturbation problem ⋮ Nonconforming polynomial mixed finite element for the Brinkman problem over quadrilateral meshes ⋮ Modified Morley method by free formula for fourth order elliptic singular perturbation problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A discrete de Rham complex with enhanced smoothness
• A robust nonconforming $H^2$-element
• On the Necessity and Sufficiency of the Patch Test for Convergence of Nonconforming Finite Elements
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem

This page was built for publication: Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems