Error Controlled Adaptive Finite Elements In Solid Mechanics PDF Download
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| Author | : Ekkehard Ramm |
| Publisher | : John Wiley & Sons |
| Total Pages | : 422 |
| Release | : 2003-08-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0470857978 |
Download Error-controlled Adaptive Finite Elements in Solid Mechanics Book in PDF, ePub and Kindle
Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering
| Author | : Erwin Stein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 2007-04-02 |
| Genre | : Technology & Engineering |
| ISBN | : 3211380604 |
Download Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics Book in PDF, ePub and Kindle
This course with 6 lecturers intends to present a systematic survey of recent re search results of well-known scientists on error-controlled adaptive finite element methods in solid and structural mechanics with emphasis to problem-dependent concepts for adaptivity, error analysis as well as h- and p-adaptive refinement techniques including meshing and remeshing. Challenging applications are of equal importance, including elastic and elastoplastic deformations of solids, con tact problems and thin-walled structures. Some major topics should be pointed out, namely: (i) The growing importance of goal-oriented and local error estimates for quan tities of interest—in comparison with global error estimates—based on dual finite element solutions; (a) The importance of the p-version of the finite element method in conjunction with parameter-dependent hierarchical approximations of the mathematical model, for example in boundary layers of elastic plates; (Hi) The choice of problem-oriented error measures in suitable norms, consider ing residual, averaging and hierarchical error estimates in conjunction with the efficiency of the associated adaptive computations; (iv) The importance of implicit local postprocessing with enhanced test spaces in order to get constant-free, i. e. absolute-not only relative-discretizati- error estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat ical modeling in related subdomains, such as boundary layers. The main goals of adaptivity are reliability and efficiency, combined with in sight and access to controls which are independent of the applied discretization methods. By these efforts, new paradigms in Computational Mechanics should be realized, namely verifications and even validations of engineering models.
| Author | : Wolfgang Bangerth |
| Publisher | : Birkhäuser |
| Total Pages | : 216 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 303487605X |
Download Adaptive Finite Element Methods for Differential Equations Book in PDF, ePub and Kindle
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
| Author | : Christian A. Möller |
| Publisher | : Logos Verlag Berlin GmbH |
| Total Pages | : 259 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 3832528156 |
Download Adaptive Finite Elements in the Discretization of Parabolic Problems Book in PDF, ePub and Kindle
Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.
| Author | : Peter Wriggers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 566 |
| Release | : 2008-09-24 |
| Genre | : Mathematics |
| ISBN | : 3540710000 |
Download Nonlinear Finite Element Methods Book in PDF, ePub and Kindle
Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 446 |
| Release | : 2024-06-29 |
| Genre | : Science |
| ISBN | : 0443294496 |
Download Error Control, Adaptive Discretizations, and Applications, Part 1 Book in PDF, ePub and Kindle
Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. Covers multi-scale modeling Includes updates on data-driven modeling Presents the latest information on large deformations of multi-scale materials
| Author | : Timothy J. Barth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 354 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662051893 |
Download Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics Book in PDF, ePub and Kindle
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
| Author | : Marcus Olavi Rüter |
| Publisher | : Springer Nature |
| Total Pages | : 496 |
| Release | : 2019-11-07 |
| Genre | : Science |
| ISBN | : 3030061736 |
Download Error Estimates for Advanced Galerkin Methods Book in PDF, ePub and Kindle
This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.
| Author | : |
| Publisher | : |
| Total Pages | : 27 |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
Download Goal-oriented Error Measures and Adaptive Finite Element Procedures in Solid Mechanics Book in PDF, ePub and Kindle
| Author | : Franz-Theo Suttmeier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 162 |
| Release | : 2009-03-12 |
| Genre | : Mathematics |
| ISBN | : 3834895466 |
Download Numerical solution of Variational Inequalities by Adaptive Finite Elements Book in PDF, ePub and Kindle
The author presents a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. The local weighted residuals, that result from an extension of the so-called Dual-Weighted-Residual method, are used in a feed-back process for generating economical meshes. Based on several model problems, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.
