Workshop Singularly Perturbed Problems
Talks & Slides
Remarks on asymptotic expansions for singularly perturbed second order ODEs with multiple scales
We consider systems of two coupled second order two point bvps with two singular perturbation parameters. For the "elliptic-elliptic" case (i.e., the equation does not involve first order terms) full asymptotic are presented that cover the full range of the two singular perturbation parameters. As an application, we show that hp-FEM can converge at a robust exponential rate (in the energy norm) on suitably designed meshes.
We will also discuss the case of "strongly coupled systems" and derive for a model situation the asymptotic expansions that reveal the layer structure.
The results presented are joint work with C. Xenophontos (Cyprus) and B. Pichler (Vienna).