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Superconvergence In Galerkin Finite Element Methods
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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 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 370 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 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 Superconvergence, Superaccuracy, and Stability of the Discontinuous Galerkin Finite Element Method by : Noel Chalmers
Download or read book Superconvergence, Superaccuracy, and Stability of the Discontinuous Galerkin Finite Element Method written by Noel Chalmers and published by . This book was released on 2015 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the investigation of the superconvergence, superaccuracy, and stability properties of the discontinuous Galerkin (DG) finite element method in one and two dimensions. We propose a novel method for the analysis of these properties. We apply the DG method to a model linear advection problem to derive a PDE which is satisfied by the numerical solution itself. This PDE is equivalent to the original advection equation but with a forcing term that is proportional to the jump in the numerical solution at the cell interfaces. We then use classical Fourier analysis to determine the solutions to this PDE with particular temporal frequencies. We find that these Fourier modes are completely determined on each cell by the inflow into that cell and a certain rational function of the mode's frequency. By using local expansions of these modes, we prove several local superconvergence properties of the DG method, as well as superaccurate errors in terms of dissipation and dispersion. Next, by considering a uniform mesh and assuming periodic boundary conditions, we investigate the spectrum of the method. In particular, we show that the spectrum can be partitioned into physical and non-physical modes. The physical modes advect with high-order accuracy while the non-physical modes decay exponentially quickly in time. Using these results we establish several global superconvergence properties of the method on uniform meshes. Finally, we also propose a new family of schemes which can been viewed as a modified version of the DG scheme. We extend our analysis to these new schemes we construct schemes with significantly larger stable CFL numbers than the classic DG method. We demonstrate through some numerical examples that these modified schemes can be effective in capturing fine structures of the numerical solution when compared with the DG scheme with equivalent computational effort.
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:
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 Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomée
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomée and published by Springer Science & Business Media. This book was released on 2010 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 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 Galerkin and Collocation-Galerkin Methods with Superconvergence and Optimal Fluxes by : G. F. Carey
Download or read book Galerkin and Collocation-Galerkin Methods with Superconvergence and Optimal Fluxes written by G. F. Carey and published by . This book was released on 1979 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are formulated and examined for Galerkin and collocation schemes and a mixed collocation-Galerkin finite element method. Superconvergence at special points is investigated and a new method for calculating optimal derivatives such as fluxes or stresses in typical applications is described and implemented for an example problem. (Author).
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781722457945 Total Pages :26 pages Book Rating :4.4/5 (579 download)
Book Synopsis On the Superconvergence of Galerkin Methods for Hyperbolic Ibvp by : National Aeronautics and Space Administration (NASA)
Download or read book On the Superconvergence of Galerkin Methods for Hyperbolic Ibvp written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed. Gottlieb, David and Gustafsson, Bertil and Olsson, Pelle and Strand, BO Unspecified Center NAS2-13721; AF-AFOSR-0090-93; N00014-91-J-4016; NSF DMS-92-11820; NUTEK-89-02539P...
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 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 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 2007-06-25 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. The revised second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.
