A modified graded mesh and higher order finite element approximation for singular perturbation problems

DOI10.1016/j.jcp.2019.04.073zbMath1452.65132OpenAlexW2952040109MaRDI QIDQ2222342

Yanyan Li

Publication date: 26 January 2021

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.04.073

zbMATH Keywords

singular perturbationfinite element methodboundary value problemlayer-adapted meshes

Mathematics Subject Classification ID

Singular perturbations of ordinary differential equations (34D15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (3)

A higher-order hybrid finite difference method based on grid equidistribution for fourth-order singularly perturbed differential equations ⋮ A modified graded mesh and higher order finite element method for singularly perturbed reaction-diffusion problems ⋮ Higher order schemes introduced to the meshless FDM in elliptic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The impact of smooth \(W\)-grids in the numerical solution of singular perturbation two-point boundary value problems
• A singularly perturbed problem with two parameters on a Bakhvalov-type mesh
• Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems
• Finite element approximation of convection-diffusion problems using an exponentially graded mesh
• B-splines with artificial viscosity for solving singularly perturbed boundary value problems
• On graded meshes for a two-parameter singularly perturbed problem
• A modification of the Shishkin discretization mesh for one-dimensional reaction-diffusion problems
• A solution of the discrepancy occurs due to using the fitted mesh approach rather than to the fitted operator for solving singularly perturbed differential equations
• Error estimates for linear finite elements on Bakhvalov-type meshes.
• Singular perturbation analysis of bistable differential equation arising in the nerve pulse propagation
• Layer-adapted meshes for reaction-convection-diffusion problems
• Derivative error bounds for Lagrange interpolation: An extension of Cauchy's bound for the error of Lagrange interpolation
• A singularly perturbed problem with two parameters in two dimensions on graded meshes
• A modified Bakhvalov mesh
• Singularly perturbed boundary-value problems.
• Finite element approximation of convection diffusion problems using graded meshes
• Grid equidistribution for reaction-diffusion problems in one dimension
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
• Uniformly convergent numerical method for singularly perturbed differential-difference equation using grid equidistribution
• Graded Meshes for Higher Order FEM
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems
• On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution

This page was built for publication: A modified graded mesh and higher order finite element approximation for singular perturbation problems