A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems

DOI10.1007/S11075-015-9969-6zbMath1333.65084OpenAlexW1983272004MaRDI QIDQ907575

Martin Stynes, Runchang Lin

Publication date: 25 January 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-9969-6

zbMATH Keywords

numerical examplesingular perturbationfinite element methodtwo-point boundary value problemShishkin meshbalanced normspline interpolantsystem of linear coupled reaction-diffusion equations

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (8)

A discontinuous Galerkin least-squares finite element method for solving coupled singularly perturbed reaction-diffusion equations ⋮ Stability and error analysis of a fully-discrete numerical method for system of 2D singularly perturbed parabolic PDEs ⋮ Numerical analysis of a fully discrete stabilized FEM for system of singularly perturbed parabolic IBVPs ⋮ Finite element analysis of singularly perturbed problems with discontinuous diffusion ⋮ A Uniformly Convergent Numerical Scheme for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations ⋮ An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems ⋮ Non-symmetric interior penalty Galerkin finite element method for a class of singularly perturbed reaction diffusion problems with discontinuous data ⋮ Numerical solutions of a system of singularly perturbed reaction-diffusion problems

Cites Work

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• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems
• A first-order system Petrov–Galerkin discretization for a reaction–diffusion problem on a fitted mesh
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems

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