# Pierre Degond : Asymptotic-Preserving numerical methods for variable-scale problems. Examples from fluids and plasma dynamics

Multiscale problems are often treated via asymptotic of homogenization techniques: one first determines the asymptotic limit and then finds an appropriate numerical methods to solve it. Variable scale problems which exhibit a continuous variation of the perturbation parameter from a finite to an infinitesimal value cannot be solved by this method alone. They require the coupling of the asymptotic problem to the original one across the region of scale variation. This coupling is often quite complex and lacks robustness. Asymptotic-Preserving methods represent an alternative to the coupling strategy and provide a way to resolve the original problem without resorting to its asymptotic limit. They provide a systematic methodology to resolve multiscale problems even in situations where the asymptotic limit is quite complex. We will provide examples of this methodology for the treatment of the low-Mach number regime, of quasineutrality in plasmas, large magnetic fields or strong anisotropy in diffusion equations.

**Category**: Applied Math and Analysis**Duration**: 01:34:50**Date**: February 15, 2010 at 4:25 PM**Views**: 111-
**Tags:**seminar, Applied Math And Analysis Seminar

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