Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Springer Science & Business Media. This book was released on 2003-01-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual 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. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2014-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Error controlled Adaptive Finite Elements in Solid Mechanics written by Ekkehard Ramm and published by John Wiley & Sons. This book was released on 2003-08-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics written by Erwin Stein and published by Springer Science & Business Media. This book was released on 2007-04-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adaptive Finite Element Methods for Multiscale Partial Differential Equations written by Achim Nonnenmacher and published by . This book was released on 2011 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Finite Elements in the Discretization of Parabolic Problems written by Christian A. Möller and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adaptive Finite Element Methods for Optimization in Partial Differential Equations written by Hartmut Kapp and published by . This book was released on 2000 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Finite Element Methods for Time Dependent Partial Differential Equations written by Slimane Adjerid and published by . This book was released on 1985 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiscale Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer. This book was released on 2014-12-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations written by Roland Becker and published by . This book was released on 1998 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Scaled Boundary Finite Element Method written by John P. Wolf and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.

Download or read book The Mathematical Theory of Finite Element Methods written by Susanne Brenner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide