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A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations. (English) Zbl 1042.65065
This paper deals with the finite element method for two coupled singularly perturbed reaction-diffusion problems on general meshes. A general criterion that guarantees parameter uniform convergence in the energy norm is presented. The authors give interpolation and approximation error bounds for arbitrary meshes. The paper concludes with supporting numerical results.

MSC:
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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