A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems

DOI10.1016/j.amc.2006.09.044zbMath1114.65344OpenAlexW2170151419MaRDI QIDQ883959

Christos Xenophontos, L. Oberbroeckling

Publication date: 12 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.09.044

zbMATH Keywords

convergencesingular perturbationfinite element methodnumerical examplesreaction-diffusion problemsboundary layersShishkin mesh\(hp\) version

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) 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) Singular perturbations for ordinary differential equations (34E15)

Related Items (15)

Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales ⋮ Discontinuous Galerkin \(h p\)-adaptive methods for multiscale chemical reactors: quiescent reactors ⋮ An iterative Tikhonov regularization for solving singularly perturbed elliptic PDE ⋮ A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Asymptotic streamline diffusion finite element method for singularly perturbed convection–diffusion differential difference equations ⋮ An Asymptotic-Numerical Method for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations ⋮ Uniform global convergence of a hybrid scheme for singularly perturbed reaction-diffusion systems ⋮ Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method ⋮ Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm ⋮ Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback ⋮ Exponentially graded mesh for a singularly perturbed problem with two small parameters ⋮ An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems ⋮ A robust domain decomposition algorithm for singularly perturbed semilinear systems ⋮ Numerical solutions of a system of singularly perturbed reaction-diffusion problems

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