ABSTRACT
The combination of asymptotic and numerical analyses provides improved accuracy for multiple-scales problems1 . Many physical problems have multiple scales; a typical situation occurs when physics on the fastest scale induces narrow regions where the variation in the solution is large. Such regions are called boundary layers or transition layers, depending on whether they are near a boundary or inside the interior of the domain. Examples of such situations are laminar flow of a slightly viscous fluid or combustion with high activation energy. Classical schemes applied to these types of situation generally fail to correctly describe the behavior inside the layers. This difficulty is overcome by developing numerical methods based on the asymptotic analysis of the multiple-scales problems. We demonstrate how asymptotic analysis and numerical analysis can interact to achieve the goal of a highly accurate solution method.
