The Least-Squares Finite Element Method
The Least-Squares Finite Element Method

Author: Bo-nan Jiang

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 425

ISBN-13: 3662037408

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This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Finite Element Methods for Flow Problems
Finite Element Methods for Flow Problems

Author: Jean Donea

Publisher: John Wiley & Sons

Published: 2003-06-02

Total Pages: 366

ISBN-13: 9780471496663

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Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.

Least-Squares Finite Element Methods
Least-Squares Finite Element Methods

Author: Pavel B. Bochev

Publisher: Springer Science & Business Media

Published: 2009-04-28

Total Pages: 669

ISBN-13: 0387689222

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Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Finite Element Methods for Computational Fluid Dynamics
Finite Element Methods for Computational Fluid Dynamics

Author: Dmitri Kuzmin

Publisher: SIAM

Published: 2014-12-18

Total Pages: 321

ISBN-13: 1611973600

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This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?

The Finite Element Method for Fluid Dynamics
The Finite Element Method for Fluid Dynamics

Author: Olek C Zienkiewicz

Publisher: Butterworth-Heinemann

Published: 2013-11-21

Total Pages: 581

ISBN-13: 0080951376

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The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems Biofluid dynamics, covering flow throughout the human arterial system Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation

Least-squares Variational Principles and the Finite Element Method
Least-squares Variational Principles and the Finite Element Method

Author: Juan Pablo Pontaza

Publisher:

Published: 2004

Total Pages:

ISBN-13:

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We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solid and fluid mechanics. For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model. Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite element model always yields a discrete system of equations with a symmetric positive definite coefficient matrix. These attributes, amongst many others highlighted and detailed in this work, allow the development of robust and efficient finite element models for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.