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Advanced Finite Element Methods with Applications

Advanced Finite Element Methods with Applications PDF Author: Thomas Apel
Publisher: Springer
ISBN: 3030142442
Category : Mathematics
Languages : en
Pages : 428
Book Description
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.

Advanced Finite Element Methods with Applications

Advanced Finite Element Methods with Applications PDF Author: Thomas Apel
Publisher: Springer
ISBN: 3030142442
Category : Mathematics
Languages : en
Pages : 428
Book Description
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.

Advanced Finite Element Methods and Applications

Advanced Finite Element Methods and Applications PDF Author: Thomas Apel
Publisher: Springer Science & Business Media
ISBN: 3642303161
Category : Technology & Engineering
Languages : en
Pages : 376
Book Description
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.

Advanced Finite Element Methods and Applications

Advanced Finite Element Methods and Applications PDF Author: Thomas Apel
Publisher: Springer
ISBN: 9783642303159
Category : Technology & Engineering
Languages : en
Pages : 376
Book Description
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.

Finite Element Method with Applications in Engineering:

Finite Element Method with Applications in Engineering: PDF Author: Y. M. Desai
Publisher: Pearson Education India
ISBN: 9332500835
Category :
Languages : en
Pages : 492
Book Description
The book explains the finite element method with various engineering applications to help students, teachers, engineers and researchers. It explains mathematical modeling of engineering problems and approximate methods of analysis and different approaches

The Finite Element Method: Theory, Implementation, and Applications

The Finite Element Method: Theory, Implementation, and Applications PDF Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 395
Book Description
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.​

Advanced Finite Element Method in Structural Engineering

Advanced Finite Element Method in Structural Engineering PDF Author: Yu-Qiu Long
Publisher: Springer Science & Business Media
ISBN: 3642003168
Category : Technology & Engineering
Languages : en
Pages : 706
Book Description
Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.

Concepts and Applications of Finite Element Analysis

Concepts and Applications of Finite Element Analysis PDF Author: Robert D. Cook
Publisher: John Wiley & Sons Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 744
Book Description
This book has been thoroughly revised and updated to reflect developments since the third edition, with an emphasis on structural mechanics. Coverage is up-to-date without making the treatment highly specialized and mathematically difficult. Basic theory is clearly explained to the reader, while advanced techniques are left to thousands of references available, which are cited in the text.

BEM-based Finite Element Approaches on Polytopal Meshes

BEM-based Finite Element Approaches on Polytopal Meshes PDF Author: Steffen Weißer
Publisher: Springer
ISBN: 303020961X
Category : Computers
Languages : en
Pages : 246
Book Description
This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.

Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018

Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 PDF Author: Gabriel R. Barrenechea
Publisher: Springer Nature
ISBN: 3030418006
Category : Mathematics
Languages : en
Pages : 254
Book Description
This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.

Optimization and Control for Partial Differential Equations

Optimization and Control for Partial Differential Equations PDF Author: Roland Herzog
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110695987
Category : Mathematics
Languages : en
Pages : 474
Book Description
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.