Product DescriptionTraditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domainspectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrateshow these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.Review"Though there is a lot of detailed technical material here, Karniadakis & Sherwin have written in a very visual style with good graphics scattered throughout the text in a helpful way. They have brought togetehr in one accessible volume a body of literature and have demonstrated the applicabilityand utility of this class of high-order numerical methods for differential equations."--Journal of Fluid MechanicsAbout the AuthorGeorge Em Karniadakis, Professor of Applied Mathematics, Brown University. Spencer J. Sherwin, Lecturer in Aeronautics, Imperial College of Science, Technology and Medicine.