Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 9780521011952

Category: Mathematics

Page: 352

View: 7914

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This is a thoroughly revised version of the successful first edition. In addition to up-dating the existing text, the author has added new material that will prove useful for research or application of the finite element method. The most important application of finite elements is the numerical solution of elliptic partial differential equations. The author gives a thorough coverage of this subject and includes aspects such as saddle point problems which require a more in-depth mathematical treatment. This is a book for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.
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Finite Element Methods for Maxwell's Equations

Author: Peter Monk,Department of Mathematics Sciences Peter Monk, PH.

Publisher: Oxford University Press

ISBN: 9780198508885

Category: Mathematics

Page: 450

View: 4231

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The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.
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Structural Analysis with Finite Elements

Author: Friedel Hartmann,Casimir Katz

Publisher: Springer Science & Business Media

ISBN: 366205423X

Category: Science

Page: 484

View: 7890

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This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.
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Theory and Practice of Finite Elements

Author: Alexandre Ern,Jean-Luc Guermond

Publisher: Springer Science & Business Media

ISBN: 1475743556

Category: Mathematics

Page: 526

View: 6487

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This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
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Robust Algebraic Multilevel Methods and Algorithms

Author: Johannes Kraus,Svetozar Margenov

Publisher: Walter de Gruyter

ISBN: 3110214830

Category: Mathematics

Page: 256

View: 6044

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This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.
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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Author: Silvestru Sever Dragomir

Publisher: Springer Science & Business Media

ISBN: 331901448X

Category: Mathematics

Page: 120

View: 8332

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Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.
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Scientific Computing with MATLAB and Octave

Author: Alfio Quarteroni,Fausto Saleri,Paola Gervasio

Publisher: Springer Science & Business Media

ISBN: 3642124305

Category: Mathematics

Page: 366

View: 470

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Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.
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Advanced Finite Element Methods and Applications

Author: Thomas Apel,Olaf Steinbach

Publisher: Springer Science & Business Media

ISBN: 3642303161

Category: Technology & Engineering

Page: 376

View: 1547

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This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.
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