Analysis of a FEM for a coupled system of singularly perturbed reaction-diffusion equations

DOI10.1007/s11075-008-9228-1zbMath1163.65054OpenAlexW2155221504MaRDI QIDQ1014368

Torsten Linss

Publication date: 27 April 2009

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

Full work available at URL: https://doi.org/10.1007/s11075-008-9228-1

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

Layer structure and the galerkin finite element method for a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales ⋮ 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 ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction-diffusion problems ⋮ Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials ⋮ A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems ⋮ A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale nature

Cites Work

• A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations.
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems
• A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems
• Sufficient conditions for uniform convergence on layer-adapted grids
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