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Author : R. B. Kellogg
Release : 1981
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis The Finite Element Method for a Singular Perturbation Problem Using Enriched Subspaces by : R. B. Kellogg
Download or read book The Finite Element Method for a Singular Perturbation Problem Using Enriched Subspaces written by R. B. Kellogg. This book was released on 1981. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jens M. Melenk
Release : 2004-10-19
Genre : Mathematics
Kind : eBook
Book Rating : 81X/5 ( reviews)
Book Synopsis hp-Finite Element Methods for Singular Perturbations by : Jens M. Melenk
Download or read book hp-Finite Element Methods for Singular Perturbations written by Jens M. Melenk. This book was released on 2004-10-19. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Author : Gung-Min Gie
Release : 2018-11-21
Genre : Mathematics
Kind : eBook
Book Rating : 387/5 ( reviews)
Book Synopsis Singular Perturbations and Boundary Layers by : Gung-Min Gie
Download or read book Singular Perturbations and Boundary Layers written by Gung-Min Gie. This book was released on 2018-11-21. Available in PDF, EPUB and Kindle. Book excerpt: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
Author : Hans-Görg Roos
Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 066/5 ( reviews)
Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Author : Kenneth I. Gross
Release : 1984-01-01
Genre : Technology & Engineering
Kind : eBook
Book Rating : 998/5 ( reviews)
Book Synopsis Mathematical Methods in Energy Research by : Kenneth I. Gross
Download or read book Mathematical Methods in Energy Research written by Kenneth I. Gross. This book was released on 1984-01-01. Available in PDF, EPUB and Kindle. Book excerpt:
