Introductory Numerical Analysis of Elliptic Boundary Value Problems
Author | : Donald Greenspan |
Publisher | : |
Total Pages | : 186 |
Release | : 1965 |
Genre | : Boundary value problems |
ISBN | : |
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Author | : Donald Greenspan |
Publisher | : |
Total Pages | : 186 |
Release | : 1965 |
Genre | : Boundary value problems |
ISBN | : |
Author | : Olaf Steinbach |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2007-12-22 |
Genre | : Mathematics |
ISBN | : 0387688056 |
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.
Author | : Jean-Pierre Aubin |
Publisher | : Courier Corporation |
Total Pages | : 386 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486457915 |
A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.
Author | : Angela Kunoth |
Publisher | : Springer Science & Business Media |
Total Pages | : 150 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 332280027X |
Diese Monographie spannt einen Bogen rund um die aktuelle Thematik Wavelets, um neueste Entwicklungen anhand aufeinander aufbauender Probleme darzustellen und das konzeptuelle Potenzial von Waveletmethoden für Partielle Differentialgleichungen zu demonstrieren.
Author | : Zohar Yosibash |
Publisher | : Springer Science & Business Media |
Total Pages | : 473 |
Release | : 2011-12-02 |
Genre | : Mathematics |
ISBN | : 146141508X |
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, is still 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.
Author | : Garrett Birkhoff |
Publisher | : SIAM |
Total Pages | : 100 |
Release | : 1971-01-01 |
Genre | : Mathematics |
ISBN | : 9780898710014 |
A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
Author | : R. Teman |
Publisher | : Springer Science & Business Media |
Total Pages | : 170 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401025657 |
This book is an introduction to one of the important as pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation. This book is not a systematic study of the subject, but the methods developed here can be applied to large classes of linear and nonlinear elliptic problems. The book assumes that the reader's knowledge of Anal ysis is comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.
Author | : Peter Knabner |
Publisher | : Springer Science & Business Media |
Total Pages | : 437 |
Release | : 2006-05-26 |
Genre | : Mathematics |
ISBN | : 0387217622 |
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Author | : Peter Knabner |
Publisher | : Springer Nature |
Total Pages | : 811 |
Release | : 2021-11-19 |
Genre | : Mathematics |
ISBN | : 3030793850 |
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.