Mixed Finite Element Methods And Applications

Author : Daniele Boffi,Franco Brezzi,Michel Fortin
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 54,9 Mb
Release : 2013-07-02
Category : Mathematics
ISBN : 9783642365195

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Mixed Finite Element Methods and Applications by Daniele Boffi,Franco Brezzi,Michel Fortin Pdf

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.

Author : Gabriel N. Gatica
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 49,6 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9783319036953

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A Simple Introduction to the Mixed Finite Element Method by Gabriel N. Gatica Pdf

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

Author : Zhangxin Chen
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 40,9 Mb
Release : 2005-10-14
Category : Science
ISBN : 9783540280781

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Finite Element Methods and Their Applications by Zhangxin Chen Pdf

Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

Author : Franco Brezzi,Michel Fortin
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461231721

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Mixed and Hybrid Finite Element Methods by Franco Brezzi,Michel Fortin Pdf

Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.

Author : Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Springer
Page : 244 pages
File Size : 43,5 Mb
Release : 2008-04-01
Category : Mathematics
ISBN : 9783540783190

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Mixed Finite Elements, Compatibility Conditions, and Applications by Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 46,9 Mb
Release : 2013-01-13
Category : Computers
ISBN : 9783642332876

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The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Author : Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publisher : Springer
Page : 428 pages
File Size : 50,5 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030142445

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Advanced Finite Element Methods with Applications by Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach Pdf

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Author : Anonim
Publisher : Unknown
Page : 18 pages
File Size : 48,6 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:76526440

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Mixed Finite Element Methods and Applications by Anonim Pdf

Author : Peter Wriggers,Carsten Carstensen
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 45,7 Mb
Release : 2009-06-16
Category : Technology & Engineering
ISBN : 9783211990940

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Mixed Finite Element Technologies by Peter Wriggers,Carsten Carstensen Pdf

Mixed finite element methods are a tool to solve complex engineering problems of different nature. This subject is treated in the volume from the engineering and the mathematical point. Different applications are considered which depict the value of mixed formulations in engineering on one side. On the other side the mathematical background is provided including proofs of convergence and stability of these methods and adequate solvers for mixed problems are discussed. This broad spectrum yields an indepth treatment of mixed methods from different perspectives.

Author : Theodore H.H. Pian,Chang-Chun Wu
Publisher : CRC Press
Page : 395 pages
File Size : 40,8 Mb
Release : 2005-11-04
Category : Mathematics
ISBN : 9781135442217

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Hybrid and Incompatible Finite Element Methods by Theodore H.H. Pian,Chang-Chun Wu Pdf

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

Author : Zhangxin Chen
Publisher : World Scientific
Page : 349 pages
File Size : 49,7 Mb
Release : 2011
Category : Technology & Engineering
ISBN : 9789814350563

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The Finite Element Method by Zhangxin Chen Pdf

A fundamental and practical introduction to the finite element method, its variants, and their applications in engineering.

Author : Anonim
Publisher : Unknown
Page : 18 pages
File Size : 54,8 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:897976768

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Mixed Finite Element Methods and Applications by Anonim Pdf

Author : J. E. Akin
Publisher : Unknown
Page : 388 pages
File Size : 47,8 Mb
Release : 1984
Category : Mathematics
ISBN : MINN:31951D002307831

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Application and Implementation of Finite Element Methods by J. E. Akin Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 51,9 Mb
Release : 2008-04-14
Category : Mathematics
ISBN : 9783540783145

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Mixed Finite Elements, Compatibility Conditions, and Applications by Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Author : Debasis Deb
Publisher : PHI Learning Pvt. Ltd.
Page : 377 pages
File Size : 47,7 Mb
Release : 2010
Category : Finite element method
ISBN : 9788120342958

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Finite Element Methods : Concepts and Applications in Geomechanics by Debasis Deb Pdf