This volume provides a record of the workshop on asymptotic-induced numerical methods for partial differential equations, critical parameters and domain decomposition, held at Beaune, France. Discussing new computational methods, recent algorithm developments, and state-of-the-art techniques in mathematical modeling, Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters explores important topics in theory and application, including: modeling of complex fluid dynamics systems; asymptotic-induced domain decomposition methods; analysis of strongly nonlinear problems; tools available for modern numerical analysis; and symbolic manipulation tools for multiscale problems. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters presents a panoramic view of areas where asymptotic analysis, numerical analysis, and scientific computing are beginning to be integrated effectively. With articles ranging from mathematical models and applications to state-of-the-art algorithms and computational methods, the book is an invaluable text for mathematicians, engineers, and computer scientists who wish to become involved in this challenging new area of research.