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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.

Reviewer: Pavol Chocholatý (Bratislava)

### 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 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 |

### Keywords:

Reaction-diffusion equation; ingular perturbation; solution decomposition; Shishkin mesh; finite element method; convergence; error bounds; numerical results
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\textit{T. Linß} and \textit{N. Madden}, Appl. Math. Comput. 148, No. 3, 869--880 (2004; Zbl 1042.65065)

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### References:

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[9] | Miller, J.J.H; O’Riordan, E; Shishkin, G.I, Fitted numerical methods for singular perturbation problems. error estimates in the maximum norm for linear problems in one and two dimensions, (1996), World Scientific Singapore · Zbl 0915.65097 |

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