Numerical Methods For Elliptic Boundary Value Problems With Singularities
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Numerical Methods For Elliptic Boundary Value Problems With Singularities
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Author : Zi-Cai Li
language : en
Publisher:
Release Date : 1986
Numerical Methods For Elliptic Boundary Value Problems With Singularities written by Zi-Cai Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Numerical Methods For Elliptic Problems With Singularities
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Author : Zi-Cai Li
language : en
Publisher: World Scientific
Release Date : 1990
Numerical Methods For Elliptic Problems With Singularities written by Zi-Cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.
Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn
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Author : Zi-cai Li
language : en
Publisher: World Scientific
Release Date : 1990-12-27
Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn written by Zi-cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-27 with Mathematics categories.
This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.
Singularities In Elliptic Boundary Value Problems And Elasticity And Their Connection With Failure Initiation
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Author : Zohar Yosibash
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-02
Singularities In Elliptic Boundary Value Problems And Elasticity And Their Connection With Failure Initiation written by Zohar Yosibash 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 2011-12-02 with Mathematics categories.
This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, isstill a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.
Spectral Problems Associated With Corner Singularities Of Solutions To Elliptic Equations
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Author : Vladimir Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Spectral Problems Associated With Corner Singularities Of Solutions To Elliptic Equations written by Vladimir Kozlov 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 2001 with Mathematics categories.
This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order 2m in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order 2 in an n-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.
Numerical Analysis Of Singularities And First Derivatives For Elliptic Boundary Value Problems In Two Dimensions
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Author : Zohar Yosibash
language : en
Publisher:
Release Date : 1994
Numerical Analysis Of Singularities And First Derivatives For Elliptic Boundary Value Problems In Two Dimensions written by Zohar Yosibash and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Differential equations, Elliptic categories.
Elliptic Problems In Nonsmooth Domains
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Author : Pierre Grisvard
language : en
Publisher: SIAM
Release Date : 1985-01-01
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 1985-01-01 with Mathematics categories.
This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic problems in nonsmooth domains: provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems, and addresses fourth-order boundary value problems and numerical treatment of singularities.
Applied Mathematics Notes
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Author :
language : en
Publisher:
Release Date : 1986
Applied Mathematics Notes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Soviet Journal Of Numerical Analysis And Mathematical Modelling
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Author :
language : en
Publisher:
Release Date : 1990
Soviet Journal Of Numerical Analysis And Mathematical Modelling written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematical models categories.
Russian Journal Of Numerical Analysis And Mathematical Modelling
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Author :
language : en
Publisher:
Release Date : 1990
Russian Journal Of Numerical Analysis And Mathematical Modelling written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematical models categories.