Eugene O'Riordan - Böcker

Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques.Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.

Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques.Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.

These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ¨ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems exhibiting solutions with layers. The Proceedings give a good overview of current research into the theory, app- cation and solution (by both numerical and asymptotic methods) of problems that involve boundaryand interior layers. In addition to invited and contributed lectures, the conference included four mini-symposia devoted to stabilized ?nite element methods, asymptotic scaling of wall-bounded ?ows, systems of singularly p- turbed differential equations, and problems with industrial applications (supported by MACSI, the Mathematics Applications Consortium for Science and Industry). These titles exemplify the mix of interests among the participants.

Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In this revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.