Elliptic Differential Equations

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Elliptic Differential Equations

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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2017-06-01

Elliptic Differential Equations written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Elliptic Partial Differential Equations Of Second Order

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Author : David Gilbarg
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-12

Elliptic Partial Differential Equations Of Second Order written by David Gilbarg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-12 with Mathematics categories.

This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.

Elliptic Differential Equations

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Author : W. Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-10-08

Elliptic Differential Equations written by W. Hackbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-08 with Language Arts & Disciplines categories.

Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom

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Author : John Arthur Trangenstein
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-18

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom written by John Arthur Trangenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.

For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Elliptic Partial Differential Equations

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Author : Vitaly Volpert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-03

Elliptic Partial Differential Equations written by Vitaly Volpert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-03 with Mathematics categories.

The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

Elliptic Partial Differential Equations

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Author : Lucio Boccardo
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29

Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.

Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.

Kernel Functions And Elliptic Differential Equations In Mathematical Physics

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Author : Stefan Bergman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-23

Kernel Functions And Elliptic Differential Equations In Mathematical Physics written by Stefan Bergman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-23 with Mathematics categories.

Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

Stable Solutions Of Elliptic Partial Differential Equations

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Author : Louis Dupaigne
language : en
Publisher: CRC Press
Release Date : 2011-03-15

Stable Solutions Of Elliptic Partial Differential Equations written by Louis Dupaigne and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-15 with Mathematics categories.

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.

Elliptic Partial Differential Equations

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Author : Qing Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Elliptic Partial Differential Equations written by Qing Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems. This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.

Numerical Solution Of Elliptic Differential Equations By Reduction To The Interface

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Author : Boris N. Khoromskij
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Solution Of Elliptic Differential Equations By Reduction To The Interface written by Boris N. Khoromskij and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.