Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : Mikhail Alekseevich Lavrentʹev
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by Mikhail Alekseevich Lavrentʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Boundary value problems categories.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : M. A. Lavrent'ev
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by M. A. Lavrent'ev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Boundary value problems categories.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : Mikhail Alekseevich Lavrent-Ev
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by Mikhail Alekseevich Lavrent-Ev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Direct Methods In The Theory Of Elliptic Equations
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Author : Jindrich Necas
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-06
Direct Methods In The Theory Of Elliptic Equations written by Jindrich Necas 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 2011-10-06 with Mathematics categories.
Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lamesystem and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
Numerical Approximation Methods For Elliptic Boundary Value Problems
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Author : Olaf Steinbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
Numerical Approximation Methods For Elliptic Boundary Value Problems written by Olaf Steinbach 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 2007-12-22 with Mathematics categories.
This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : Mikhail Mikhaĭlovich Lavrentʹev
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by Mikhail Mikhaĭlovich Lavrentʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Boundary value problems categories.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : Mikhail Alekseevich Lavrentv
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by Mikhail Alekseevich Lavrentv and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Boundary value problems categories.
Unified Transform For Boundary Value Problems
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Author : Athanasios S. Fokas
language : en
Publisher: SIAM
Release Date : 2014-12-30
Unified Transform For Boundary Value Problems written by Athanasios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations Authorized Translation From The Russian Edited By J R M Radok
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Author : Mikhail Alekseevich Lavrent'ev
language : en
Publisher:
Release Date : 1963
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations Authorized Translation From The Russian Edited By J R M Radok written by Mikhail Alekseevich Lavrent'ev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Elliptic Problems In Nonsmooth Domains
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Author : Pierre Grisvard
language : en
Publisher: SIAM
Release Date : 2011-10-20
Elliptic Problems In Nonsmooth Domains written by Pierre Grisvard and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-20 with Mathematics categories.
Originally published: Boston: Pitman Advanced Pub. Program, 1985.