We study a family of singular perturbation problems of the kind inf { 1 ε ∫ Ω f(u, ε∇u, ερ) dx : ∫

It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular perturbation problem admits a decomposition into a regular part and a finite linear combination of explicit singular functions. Taking into acco...

We consider the approximation of systems of singularly perturbed reaction-diffusion equations, with the finite element method. The solution to such problems contains, in general, boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. In t...

An introduction to some recently developed methods for the analysis of systems of singularly perturbed ordinary differential equations is given in the context of a specific problem describing glycolytic oscillations. In suitably scaled variables the governing equations are a planar system of ordinary differential equations depending singularly on two small parameters ε and δ. In [20] it was arg...