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On The Convergence And Superconvergence Of The Generalized Finite Element Methods
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Book Synopsis On the Convergence and Superconvergence of the Generalized Finite Element Methods by : Cosmin Anitescu
Download or read book On the Convergence and Superconvergence of the Generalized Finite Element Methods written by Cosmin Anitescu and published by . This book was released on 2010 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods by : Michel Krizek
Download or read book Finite Element Methods written by Michel Krizek and published by Routledge. This book was released on 2017-11-22 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.
Book Synopsis Superconvergence in the Generalized Finite Element Method by :
Download or read book Superconvergence in the Generalized Finite Element Method written by and published by . This book was released on 2005 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions. In particular, we show that the superconvergence points for the gradient of the approximate are zeros of certain systems of non-linear equations that do not depend on the solution of the boundary value problem. For approximate solutions with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate solution as the roots of certain systems of non-linear equations. We note that it is easy to construct smooth generalized finite element approximation.
Book Synopsis Superconvergence in Galerkin Finite Element Methods by : Lars Wahlbin
Download or read book Superconvergence in Galerkin Finite Element Methods written by Lars Wahlbin and published by Springer. This book was released on 2006-11-14 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.
Book Synopsis Superconvergence in Galerkin Finite Element Methods by : Lars B. Wahlbin
Download or read book Superconvergence in Galerkin Finite Element Methods written by Lars B. Wahlbin and published by . This book was released on 1995 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles by :
Download or read book N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles written by and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we introduce a new definition of super convergence - the n%-superconvergence, which generalizes the classical idea of superconvergence to general meshes. We show that this new definition can be employed to determine the regions of least error in any element in the interior of any grid by using a computer-based approach. We present numerical results for the standard displacement finite element method for the scalar equation of orthotropic heat- conduction. The results demonstrate that n% superconvergence is applicable to the complex grids which are employed in practical engineering computations.
Book Synopsis Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) by : John J H Miller
Download or read book Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) written by John J H Miller and published by World Scientific. This book was released on 2012-02-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Book Synopsis Superconvergence Of Finite Element Approximations For PDEs by : Rabee Jari
Download or read book Superconvergence Of Finite Element Approximations For PDEs written by Rabee Jari and published by LAP Lambert Academic Publishing. This book was released on 2013-01 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) is a discretization technique for solving partial differential equations. It widely used in many fields of engineering such as computational fluid dynamics. The superconvergence of finite element solutions is an interesting and useful phenomenon in the scientific computing of real world problems and has become an area of active research in recent years. A general superconvergence of discontinuous Galerkin finite element method for the elliptic problem is established by using L DEGREES2-projection method. Regularity assumptions for the elliptic problem with regular partitions are required. Numerical experiments are given to verify the theoretical resu
Book Synopsis Superconvergence in Finite Element Methods and Meshes which are Locally Symmetric with Respect to a Point by : Alfred H. Schatz
Download or read book Superconvergence in Finite Element Methods and Meshes which are Locally Symmetric with Respect to a Point written by Alfred H. Schatz and published by . This book was released on 1994 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Smoothed Finite Element Methods by : G.R. Liu
Download or read book Smoothed Finite Element Methods written by G.R. Liu and published by CRC Press. This book was released on 2016-04-19 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve mo
Book Synopsis Finite Element Methods by : Ningning Yan
Download or read book Finite Element Methods written by Ningning Yan and published by Alpha Science International, Limited. This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give an essentially self-contained presentation of the mathematical theory underlying the global superconvergence analysis and the recovery type a posteriori error estimates. The book tries to summarize most of the research results on global superconvergence analysis completed by the author and her colleagues, especially by Professor Q. Lin's group. The most basic material in this book is taken from another earlier Chinese book, entitled Structure and Analysis of Efficient Finite Element Methods, written by Professor Q. Lin and author in 1996. Instead of using the Green function theory as the theoretical basis as in most other earlier books on superconvergence, the global superconvergence analysis in this book is based on the so-called integral identity technique. For a posteriori error estimates, this book focuses on the recovery type a posteriori error estimate, which is more close to the superconvergence analysis in its theoretical analysis. This book is intended for postgraduate and graduate students, university teachers, scientists and engineers, who study or are engaged in computational mathematics, computational mechanics, applied mathematics, scientific and engineering computation or other related special fields. A desirable mathematical background for reading this book includes the basic knowledge of partial differential equations, functional analysis, numerical PDE, including Sobolev spaces and finite element theory. But because this book does not use the very deep mathematical theory, it also can be understood by students and engineers who are only familiar with calculus.
Book Synopsis Mathematical Aspects of Finite Element Methods by : I. Galligani
Download or read book Mathematical Aspects of Finite Element Methods written by I. Galligani and published by Springer. This book was released on 2006-11-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomee
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Book Synopsis Robust Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos
Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Book Synopsis Convergence Analysis of the Generalized Finite Element Method with Global-local Enrichments by : Varun Gupta
Download or read book Convergence Analysis of the Generalized Finite Element Method with Global-local Enrichments written by Varun Gupta and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The global-local analysis procedure in the Finite Element Method is broadly used in industry for the analysis of cracks or localized stress concentrations in large, complex, three-dimensional domains. However, the limitations of this technique are well-known. The global-local FEM (GL-FEM) involves two steps: First, the solution of the given problem is computed on a coarse, global, quasi-uniform mesh, in which the cracks or other local features need not be discretized. The solution of this problem is then used as boundary conditions to solve another Finite Element problem, which is basically a local sub-domain, comprised of localized features (like cracks), extracted from the global domain.The efficacy of the so-called Generalized Finite Element Method (GFEM) in solving such multi-scale problems has been quite well proven in past few years. Therefore, combining the two approaches, going one step further from Global-Local Finite Element Analysis, and using the local solution as an enrichment function for the global problem through the Partition of Unity framework of the Generalized Finite Element Method, gives rise to the Generalized Finite Element Method with global-local enrichments (or GFEMg-l). As these classes of methods are relatively new, there are many issues which need to be addressed to make these methods robust enough for their industrial applicability in a comprehensive manner. One of the issues surrounding this GFEMg-l approach concerns the domain size of the local problem containing the complex localized features of a structural problem, and the focus of this study is to provide guidance to address this issue. This study focuses on coming up with guidelines for selecting the size of the enrichment zone for three-dimensional fracture mechanics problems. A theoretical proof and rigorous convergence studies are presented here to provide the guidelines for selecting the size of enrichment zone for practical problems. The effect of inexact boundary conditions, applied to the local problem, on the solution is also investigated.
Book Synopsis Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids by : Jichun Li
Download or read book Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids written by Jichun Li and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Superconvergence Up to Boundaries in Finite Element Methods by : Lars B. Wahlbin
Download or read book On Superconvergence Up to Boundaries in Finite Element Methods written by Lars B. Wahlbin and published by . This book was released on 1991 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
