A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem
type: Item
instance of: scholarly article
title: A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem
zbMATH Open document ID: 0937.65114
DOI: 10.1016/S0898-1221(99)00226-6
publication date: 2000-01-20T00:00:00Z
review text: The authors construct a bilinear finite element method based on a special piecewise uniform mesh in order to solve a quasilinear singularly perturbed elliptic boundary value problem in two-space dimensions. They obtain a quasi-optimal global uniform convergence rate which is independent with regard to the perturbation parameter. In fact, they generalize their older results concerning linear cases.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1391658
zbMATH Keywords: finite element method
zbMATH Keywords: singular perturbation
zbMATH Keywords: uniform convergence
zbMATH Keywords: quasilinear
author: Jichun Li
author: I. M. Navon
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: Q5509552
cites work: Q4326386
cites work: Q4040919
cites work: Perturbations singulières dans les problèmes aux limites et en contrôle optimal
cites work: Singular perturbation analysis of discrete control systems
cites work: Applications of the Maximum Principle to Singular Perturbation Problems
cites work: Singular perturbation methods for ordinary differential equations
cites work: On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
cites work: Q4865485
cites work: Q4871736
cites work: Q3882388
cites work: Nonlinear Singular Perturbation Problems and One Sided Difference Schemes
cites work: Q3994561
cites work: Effective spectral approximations of convection-diffusion equations
cites work: Spectral elements for transport-dominated equations
cites work: Accurate Discretization for Singular Perturbations: The One-Dimensional Case
cites work: High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
cites work: A novel nonconforming uniformly convergent finite element method in two dimensions
cites work: Q3862348
cites work: On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
cites work: A finite element method for a singularly perturbed boundary value problem
cites work: The $p$ and $hp$ versions of the finite element method for problems with boundary layers
cites work: Optimal Approximability of Solutions of Singularly Perturbed Two-Point Boundary Value Problems
cites work: Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
cites work: Layer-Adapted Grids for Singular Perturbation Problems
cites work: Q4836700
cites work: Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type
cites work: A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
cites work: Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type
cites work: Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem
cites work: A numerical method for solving quasilinear elliptic equations with a small parameter for the highest derivatives
cites work: Quasilinear singularly perturbed elliptic equations in a rectangle
cites work: Q4100478
cites work: Q4148920
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391658