Adaptive Finite Element Methods For Differential Equations
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Author |
: Wolfgang Bangerth |
Publisher |
: Birkhäuser |
Total Pages |
: 216 |
Release |
: 2013-11-11 |
ISBN-10 |
: 9783034876056 |
ISBN-13 |
: 303487605X |
Rating |
: 4/5 (56 Downloads) |
Synopsis Adaptive Finite Element Methods for Differential Equations by : Wolfgang Bangerth
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 |
: Ekkehard Ramm |
Publisher |
: John Wiley & Sons |
Total Pages |
: 422 |
Release |
: 2003-08-01 |
ISBN-10 |
: 9780470857977 |
ISBN-13 |
: 0470857978 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Error-controlled Adaptive Finite Elements in Solid Mechanics by : Ekkehard Ramm
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 |
: Ekkehard Ramm |
Publisher |
: John Wiley & Sons |
Total Pages |
: 436 |
Release |
: 2002-12-30 |
ISBN-10 |
: 9780471496502 |
ISBN-13 |
: 0471496502 |
Rating |
: 4/5 (02 Downloads) |
Synopsis Error-controlled Adaptive Finite Elements in Solid Mechanics by : Ekkehard Ramm
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 |
: Ronald DeVore |
Publisher |
: Springer |
Total Pages |
: 0 |
Release |
: 2014-12-04 |
ISBN-10 |
: 3642424570 |
ISBN-13 |
: 9783642424571 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Multiscale, Nonlinear and Adaptive Approximation by : Ronald DeVore
. . . . . . . . . . . . . . . . . . . 7 7 Hyperbolic partial differential equations and conservation laws . . . 8 8 Engineering collaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 Thepresent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 Finalremarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Publications by Wolfgang Dahmen (as of summer 2009). . . . . . . . . . . . . . . 10 The way things were in multivariate splines: A personal view. . . . . . . . . . . 19 Carl de Boor 1 Tensor product spline interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Quasiinterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 MultivariateB-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Kergininterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author |
: Erwin Stein |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 368 |
Release |
: 2007-04-02 |
ISBN-10 |
: 9783211380604 |
ISBN-13 |
: 3211380604 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics by : Erwin Stein
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 |
: Slimane Adjerid |
Publisher |
: |
Total Pages |
: 142 |
Release |
: 1985 |
ISBN-10 |
: OCLC:1150091785 |
ISBN-13 |
: |
Rating |
: 4/5 (85 Downloads) |
Synopsis Adaptive Finite Element Methods for Time Dependent Partial Differential Equations by : Slimane Adjerid
Author |
: Christian A. Möller |
Publisher |
: Logos Verlag Berlin GmbH |
Total Pages |
: 259 |
Release |
: 2011 |
ISBN-10 |
: 9783832528157 |
ISBN-13 |
: 3832528156 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Adaptive Finite Elements in the Discretization of Parabolic Problems by : Christian A. Möller
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 |
: Anders Logg |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 723 |
Release |
: 2012-02-24 |
ISBN-10 |
: 9783642230998 |
ISBN-13 |
: 3642230997 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author |
: Achim Nonnenmacher |
Publisher |
: |
Total Pages |
: 195 |
Release |
: 2011 |
ISBN-10 |
: OCLC:759842315 |
ISBN-13 |
: |
Rating |
: 4/5 (15 Downloads) |
Synopsis Adaptive Finite Element Methods for Multiscale Partial Differential Equations by : Achim Nonnenmacher
Author |
: Pavel B. Bochev |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 669 |
Release |
: 2009-04-28 |
ISBN-10 |
: 9780387689227 |
ISBN-13 |
: 0387689222 |
Rating |
: 4/5 (27 Downloads) |
Synopsis Least-Squares Finite Element Methods by : Pavel B. Bochev
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.