Download or read book A Posteriori Finite Element Bounds with Adaptive Mesh Refinement Application to Outputs of the Three Dimensional Convection diffusion Equation written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Posteriori Finite Element Bounds with Adaptive Mesh Refinement Application to Outputs of the Three Dimensional Convection diffusion Equation written by Hae-Won Choi and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations based on an 'a posteriori' finite element bound method with adaptive mesh refinement is presented for linear-functional outputs of the convection-diffusion equation in three spaces dimensions. The bound method is based upon the construction of an augmented Lagrangian, in which the objective is an energy reformulation of the desired output, and the constraints are the finite element equilibrium equations and inter-subdomain continuity requirements. Outputs are functionals of the field solution obtained from partial differential equations. The bound method provides relevant, quantitative, inexpensive. And rigorous bounds to the output on a very fine discretization at a cost of the coarse mesh calculation. To achieve a derived accuracy of the bound gap at a reasonable coat, an adaptive mesh refinement technique is used to refine the mesh only where high resolution is needed. Optimal stabilization parameter [kappa]* is also studied. This parameter improves the bounds, i.e. improves the sharpness of the bound gap. Finally the hybrid flux calculations on the coarse "working" mesh are compared with that on the fine "truth" mesh.
Download or read book Computational Fluid Dynamics 2004 written by Clinton Groth and published by Springer Science & Business Media. This book was released on 2006-09-27 with total page 853 pages. Available in PDF, EPUB and Kindle. Book excerpt: Those interested in state of the art in computational fluid dynamics will find this publication a valuable source of reference. The contributions are drawn from The International Conference on Computational Fluid Dynamics (ICCFD) held in 2004. The conference is staged every two years and brings together physicists, mathematicians and engineers who review and share recent advances in mathematical and computational techniques for modeling fluid dynamics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Mathematics and Advanced Applications 2011 written by Andrea Cangiani and published by Springer Science & Business Media. This book was released on 2013-01-20 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
Download or read book A Posteriori Finite Element Bounds microform Application to Outputs of the Three dimensional Navier Stokes Equations written by Zhong Cheng and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2003 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Finite Element Method Its Basis and Fundamentals written by O. C. Zienkiewicz and published by Butterworth-Heinemann. This book was released on 2013-08-31 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: - Weak forms - Variational forms - Multi-dimensional field problems - Automatic mesh generation - Plate bending and shells - Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. - A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development - Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience - Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms
Download or read book Adaptive Mesh Refinement Based on a Posteriori Error Estimation written by Martin Juhas and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1998 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Layer Adapted Meshes for Reaction Convection Diffusion Problems written by Torsten Linß and published by Springer. This book was released on 2009-11-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
Download or read book 38th Aerospace Sciences Meeting and Exhibit written by and published by . This book was released on 2000 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local mesh Local order Adaptive Finite Element Methods with a Posteriori Error Estimators for Elliptic Partial Differential Equations written by Alan Weiser and published by . This book was released on 1981 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional error estimates for the finite element solution of elliptic partial differential equations are a priori, and little information is available from them about the actual error in a specific approximation to the solution. In recent years, locally-computable a posteriori error estimators have been developed, which apply to the actual errors committed by the finite element method for a given discretization. These estimators lead to algorithms in which the computer itself adaptively decides how and when to generate discretizations. So far, for two-dimensional problems, the computer-generated discretizations have tended to use either local mesh refinement, or local order refinement, but not both. In this thesis, we present a new class of local-mesh, local-order, square finite elements which can easily accommodate computer-chosen discretizations. We present several new locally-computable a posteriori error estimators which, under reasonable assumptions, asymptotically yield upper bounds on the actual errors committed, and algorithms in which the computer uses the error estimators to adaptively produce sequences of local-mesh, local-order discretizations.
Download or read book An Analysis of a Finite Element Method for Convection Diffusion Problems Part II A Posteriori Error Estimates and Adaptivity written by W. G. Szymczak and published by . This book was released on 1983 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: A posteriori error estimates are derived for the finite element method presented in Part I. These estimates are proven to have the property that the effectivity index theta = (error estimate/true error) converges to one as the maximum mesh size goes to zero. An adaptive mesh refinement strategy is based on equilibriating local error indicators whose sum comprises the global error estimate. Numerical results show that theta is nearly one even on coarse meshes, and that optimal meshes are created by the adaptive procedure. The successful solution of a non linear problem-modelling flow through an expanding duct, makes evident the robustness of the method. (Author).
Download or read book Adaptive Mesh Refinement Theory and Applications written by Tomasz Plewa and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Download or read book An Analysis of a Finite Element Method for Convection Diffusion Problems Part I Quasi Optimality written by W. G. Szymczak and published by . This book was released on 1983 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed analysis is performed for a finite element method applied to the general one-dimensional convection diffusion problem. Piecewise polynomials are used for the trial space. The test space is formed by locally projecting L-spline basis functions onto upwinded polynomials. The error is measured in the LP mesh dependent norm. The method is proven to be quasi-optimal (yielding nearly the best approximation from the trial space), provided that the input data is piecewise smooth. This assumption is usually observed in practice. These results are used to establish a posteriori error estimates and an adaptive mesh refinement strategy in Part II of this series (35). (Author).
Download or read book Adaptive Mesh Refinement for Finite Element Flow Modeling in Complex Geometries written by Sujata Prakash and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive mesh refinement is a powerful tool for obtaining the highest solution accuracy for a given computational effort. Over the past decade, many adaptive techniques have been developed and applied to a variety of fluid flow problems. Results obtained for compressible flows, and to an extent, 2D incompressible flows have been impressive, however, similar progress has not been noted for 3D incompressible flows, particularly in complicated geometries. The objective of this thesis was to develop and test an adaptive solution methodology for 3D incompressible flow simulations in domains of arbitrary complexity. To characterize the finite element solution error, the Zienkiewicz-Zhu patch recovery error estimator (LPR) was adopted. An enhanced version of the LPR error estimator was formulated and implemented using 10-noded tetrahedral elements. The enhanced estimator (LPRC) resulted in significantly improved gradient recovery (and consequently, improved error estimates) at virtually no additional computational cost. For mesh refinement, an elemental subdivision procedure was implemented. To enable refinement in complex geometries, a procedure for preserving the boundary integrity of a refined mesh was developed. This methodology can be used for geometric data from any solid modeling (CAD) system provided the data can be exported in the IGES format. A benchmark study of the AMR procedure, in which steady flow over a three-dimensional backward-facing step was simulated, showed that the cumulative computational effort required in the adaptive analysis was lower than that required in a non-adaptive analysis of the same problem. In the second phase of this work, the AMR procedure was applied to modeling flow through two arterial geometries. Specifically, flows in an idealized end-to-side anastomosis and in a human right coronary artery were examined. Both studies assessed whether an AMR analysis could achieve more accurate solutions than conventional analyses that utilize high-resolution meshes whose gradation is based on 'a priori' knowledge of the flow field. It was noted that mesh-independent velocity fields were not very difficult to obtain even in the absence of an adaptive methodology. However, wall shear stress fields were much more difficult to absolutely resolve non-adaptively. Given that shear stresses occurring on arterial walls are widely believed to be a key factor governing the development of arterial disease, it is very important to accurately resolve wall shear stress fields if confidence can be placed in the results of numerical simulations of arterial flow phenomena. These results indicate that wall shear stress is an extremely sensitive measure of spatial resolution, and that the systematic solution-adaptive methodology developed in this thesis is very effective in producing accurately resolved wall shear stress fields.
Download or read book A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial differential equation Outputs written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1998 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
