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:

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.

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.

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 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.

Download or read book Finite Element Methods written by 林群 and published by Elsevier. This book was released on 2007-11-28 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed by Elsevier Science on behalf of Science Press. This book discusses the accuracy of various finite element approximations and how to improve them, with the help of extrapolations and super convergence's post-processing technique. The discussion is based on asymptotic expansions for finite elements and finally reduces to the technique of integration by parts, embedding theorems and norm equivalence lemmas. The book is also devoted to explaining the origin of theorems. Masterly exposition of the accuracy and improvement of finite element methods, highlighting the postprocessing Emphasis on understanding of higher knowledge Accessible to students, engaging for experts and professionals Written by leading Chinese mathematicians, available internationally for the first time

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:

Download or read book Finite Element Solution of Boundary Value Problems written by O. Axelsson and published by SIAM. This book was released on 2001-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: a thorough, balanced introduction to both the theoretical and the computational aspects of the topic.

Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.

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.

Download or read book Boundary and Finite Elements written by J. Raamachandran and published by CRC Press. This book was released on 2000 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The main topics covered are: approximate methods in structural mechanics; finite element method; and boundary element method." "Advanced undergraduate and postgraduate students, and practicing engineers studying/working in the areas of approximate methods in structural mechanics, the boundary element and the finite element will find the book to be most useful."--BOOK JACKET.

Download or read book On the Convergence of the Boundary Element Method written by Nilotpal Ghosh and published by . This book was released on 1982 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems written by Clemens Pechstein and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to give a detailed and self-contained presentation of these methods, including the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed that have not been covered in any monograph yet: the coupling of finite and boundary elements within the tearing and interconnecting framework including exterior problems, and the case of highly varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book offers a detailed view to an active and up-to-date area of research.

Download or read book Mathematical Theory of Finite and Boundary Element Methods written by Alfred H. Schatz and published by Birkhauser. This book was released on 1990 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simplicial Partitions with Applications to the Finite Element Method written by Jan Brandts and published by Springer Nature. This book was released on 2020-10-05 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields. These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.

Download or read book The mathematics of finite elements and Applications V written by J Whiteman and published by Elsevier. This book was released on 2012-12-02 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics of Finite Elements and Applications V is the summary of invited papers and the abstracts of the poster papers in the fifth conference on The Mathematics of Finite Elements and Applications, MAFELAP 1984, held at Brunei University in May 1984. Said symposium discussedfield of finite elements, including its techniques, theory, application, and implementation . The coverage of the book includes a wide range of mathematical topics under finite elements, including its method, calculations, analysis, and applications. The book also encompasses topics of computer-generated geometric design interface; modeling in an integrated computer design; and determination of dimensional field lines. Acidized channels in chalk formations, elastodynamics, stress analysis, and infinite elements are also discussed. The book also looks at isoparametric and hierarchical element procedures and Petrov-Galerkin methods. The text is recommended for mathematicians, engineers, and those in the field of information technology who would like to know more about finite elements and its applications in their respective fields.

Download or read book Recent Advances in Computational Sciences written by Palle E. T. J0rgensen and published by World Scientific. This book was released on 2008 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrodinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book. This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.