Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type

DOI10.1016/S0045-7825(97)00329-0zbMath0936.65134OpenAlexW2140764575MaRDI QIDQ1808065

Jichun Li, I. Michael Navon

Publication date: 30 November 1999

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(97)00329-0

zbMATH Keywords

numerical resultssingular perturbationfinite element methoduniform convergenceboundary layerasymptotic expansion methodstreamline diffusion FEMShishkin type mesh

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

Novel fitted operator finite difference methods for singularly perturbed elliptic convection–diffusion problems in two dimensions, A posteriori error estimation based on conservative flux reconstruction for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem on anisotropic meshes, Three-dimensional Haar wavelet method for singularly perturbed elliptic boundary value problems on non-uniform meshes, Corrigendum to ``Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type [Comput. Math. Appl. 35 (3) (1998) 57-70], A robust finite element method for a singularly perturbed elliptic problem with two small parameters, Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type, Parameter-uniform numerical scheme for singularly perturbed parabolic convection-diffusion Robin type problems with a boundary turning point, A brief survey on numerical methods for solving singularly perturbed problems, A tailored finite point method for a singular perturbation problem on an unbounded domain, Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensions, Numerical modeling of the boundary value problem of an ordinary differential equation with a small parameter at the highest derivative by Chebyshev polynomials of the second kind, Supercloseness and post-processing of finite element method in a balanced norm for singularly perturbed reaction-diffusion equation, A new stabilized finite element formulation for scalar convection-diffusion problems: the streamline and approximate upwind/Petrov-Galerkin method., A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem, Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements, BDDC algorithms for advection-diffusion problems with HDG discretizations, Tailored finite point method based on exponential bases for convection-diffusion-reaction equation, A posteriori error estimates for one-dimensional convection-diffussion problems, Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems, Tikhonov regularization of an elliptic PDE, Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems, An arbitrary order uniformly convergent finite element method for singular perturbation problems, A quintic spline collocation method for solving time-dependent convection-diffusion problems, Uniform stability of the SUPG method for the evolutionary convection-diffusion-reaction equation, Lardy's regularization of a singularly perturbed elliptic PDE, An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem

Uses Software

• ITSOL
• SPARSKIT

Cites Work

• Finite element methods for linear hyperbolic problems
• An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
• Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type
• The hierarchical basis multigrid method for convection-diffusion equations
• Singular perturbation methods for ordinary differential equations
• Special meshes for finite difference approximations to an advection- diffusion equation with parabolic layers
• Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers
• Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem
• Bubble functions prompt unusual stabilized finite element methods.
• Multiple scale and singular perturbation methods
• Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem
• A Globally Uniformly Convergent Finite Element Method for a Singularly Perturbed Elliptic Problem in Two Dimensions
• Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods
• Asymptotic Analysis of a Singular Perturbation Problem
• Quadratic finite element schemes for two-dimensional convective-transport problems
• On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
• Accurate Discretization for Singular Perturbations: The One-Dimensional Case
• Optimal Approximability of Solutions of Singularly Perturbed Two-Point Boundary Value Problems
• High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• A note on the conditioning of upwind schemes on Shishkin meshes
• Regular degeneration and boundary layer for linear differential equations with small parameter
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item