An elliptic singularly perturbed problem with two parameters. II: Robust finite element solution

DOI10.1016/j.cam.2006.12.013zbMath1151.35021OpenAlexW2028649611MaRDI QIDQ2468140

Ljiljana Teofanov, Hans-Goerg Roos

Publication date: 30 January 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.12.013

zbMATH Keywords

singular perturbationfinite element methodconvection-diffusion problemsShishkin meshtwo small parameters

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Diffusion and convection (76R99)

Related Items

Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D ⋮ An elliptic singularly perturbed problem with two parameters. I: Solution decomposition ⋮ Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems ⋮ Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ An $hp$ finite element method for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters ⋮ An \textit{hp} finite element method for a two-dimensional singularly perturbed boundary value problem with two small parameters ⋮ SDFEM for an elliptic singularly perturbed problem with two parameters ⋮ A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem ⋮ High order multiplication perturbation method for singular perturbation problems ⋮ A singularly perturbed problem with two parameters on a Bakhvalov-type mesh ⋮ On graded meshes for a two-parameter singularly perturbed problem ⋮ A singularly perturbed problem with two parameters in two dimensions on graded meshes ⋮ Mixed finite element analysis for the Poisson-Nernst-Planck/Stokes coupling ⋮ Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh ⋮ A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems ⋮ Numerical study of two-parameter singularly perturbed problem in two dimensions on an exponentially graded mesh

Cites Work

• Error estimates for linear finite elements on Bakhvalov-type meshes.
• A robust finite element method for a singularly perturbed elliptic problem with two small parameters
• Anisotropic interpolation with applications to the finite element method
• A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes
• Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters.
• An elliptic singularly perturbed problem with two parameters. I: Solution decomposition
• Grid approximation of elliptic convection-diffusion equations in an unbounded domain with boundary layers of different types
• A parameter robust second order numerical method for a singularly perturbed two-parameter problem
• Solution of a boundary value problem for an elliptic equation with a small parameter for the leading derivatives
• Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
• The Sdfem for a Convection-diffusion Problem with Two Small Parameters
• Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes
• A Robust Method of Improved Order for Convection-Diffusion Problems in a Domain with Characteristic Boundaries
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• Grid approximation of a singularly perturbed elliptic convection–diffusion equation in an unbounded domain
• Numerical methods on Shishkin meshes for linear convection-diffusion problems
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
• A higher-order scheme for quasilinear boundary value problems with two small parameters
• Optimal convergence of basic schemes for elliptic boundary value problems with strong parabolic layers.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item