Download or read book Preconditioning of Nonconforming Finite Element Methods for Second order Elliptic Boundary Value Problems written by Sze-Ping Wong and published by . This book was released on 1992 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Approaches to Nonconforming Finite Element Discretizations of Linear Second Order Elliptic Boundary Value Problems written by Barbara Wohlmuth and published by . This book was released on 1993 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We consider adaptive multilevel techniques for nonconforming finite element discretizations of second order elliptic boundary value problems. In particular, we will focus on two basic ingredients of an efficient adaptive algorithm. The first one is the iterative solution of the arising linear system by preconditioned conjugate gradient methods and the second one is an a posteriori error estimator for the global discretization error. Both element-oriented and edge-oriented estimators will be investigated. Their local contributions will serve as an indicator within the refinement process. Finally, some numerical results will be presented. They illustrate the performance of the preconditioners as well as the refinement process."
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Download or read book Finite Element Solution of Boundary Value Problems written by O. Axelsson and published by Academic Press. This book was released on 2014-05-10 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.
Download or read book Substructuring Preconditioning for Finite Element Approximations of Second Order Elliptic Problems I Nonconforming Linear Elements for the Poisson Equation in a Parallelepiped written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains written by Hengguang Li and published by Springer Nature. This book was released on 2022-09-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.
Download or read book A Least Squares Method for Mixed Variational Formulations of Partial Differential Equations written by Jacob Jacavage and published by . This book was released on 2019 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a general framework for solving mixed variational formulations of partial differential equations. The method relates the theories of least squares finite element methods, approximating solutions to elliptic boundary value problems, and approximating solutions to symmetric saddle point problems. A general preconditioning strategy for the proposed framework is also given that utilizes the theory of multilevel preconditioners. One of the main advantages of the method is that an inf-sup condition is automatically satisfied at the discrete level for standard choices of test and trial spaces. Another benefit is that the method allows for the use of nonconforming trial spaces. In addition, the framework allows the freedom to choose the inner product on the test space, which is useful when solving PDEs, or first order systems of PDEs, with parameters and/or discontinuous coefficients. The proposed iterative solver does not require explicit bases for the trial spaces as well. Applications of the method to second order elliptic interface problems, reaction diffusion equations, and time-harmonic Maxwell's equations are presented. Numerical results in 2D and 3D, for both convex and non-convex domains, are given to support the methodology, including problems with discontinuous or highly oscillatory coefficients, low regularity of the solution, and boundary layers.
Download or read book Domain Decomposition Methods for Nonconforming Finite Element Discretizations written by Jinsheng Gu and published by Nova Publishers. This book was released on 1999 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition refers to numerical methods for obtaining solutions of scientific and engineering problems by combining solutions to problems posed on physical subdomains, or, more generally, by combining solutions to appropriately constructed subproblems. It has been a subject of intense interest recently because of its suitability for implementation on high performance computer architectures. It is well known that the nonconforming finite elements are widely used in and effective for the solving of partial differential equations derived from mechanics and engineering, because they have fewer degrees of freedom, simpler basis functions and better convergence behavior. But, there has been no extensive study of domain decomposition methods with nonconforming finite elements which lack the global continuity. Therefore, a rather systematic investigation on domain decomposition methods with nonconforming elements is of great significance and this is what the present book achieves. The theoretical breakthrough is the establishment of a series of essential estimates, especially the extension theorems for nonconforming elements, which play key roles in domain decomposition analysis. There are also many originalities in the design of the domain decomposition algorithms for the nonconforming finite element discretizations, according to the features of the nonconforming elements. The existing domain decomposition methods developed in the conforming finite element discrete case can be revised properly and extended to the nonconforming finite element discrete case correspondingly. These algorithms, nonoverlap or overlap, are as efficient as their counterparts in the conforming cases, and even easier in implementation.
Download or read book A Theoretical and Numerical Study of Nonconforming Finite Element Methods for Elliptic Boundary Value Problems written by Marcel Basil Finan and published by . This book was released on 1987 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis will comprise a theoretical and numerical study of nonconforming finite element methods. These methods are used to approximate the solution of one dimensional and two dimensional elliptic boundary value problem. Questions of existence and uniqueness of the approximation will be addressed, and the errors they entail will be analyzed. In addition computational aspects in solving the resulting systems of linear equations will be considered and numerical results will be presented.
Download or read book Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems written by Ronald H. W. Hoppe and published by . This book was released on 1994 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. By a well known postprocessing technique the discrete problem is equivalent to a modified nonconforming discretization which is solved by preconditioned cg-iterations using a multilevel BPX-type preconditioner designed for standard nonconforming approximations. Local refinement of the triangulations is based on an a posteriori error estimator which can be easily derived from superconvergence results. The performance of the preconditioner and the error estimator is illustrated by several numerical examples."
Download or read book Mixed hybrid finite element approximations of second order elliptic boundary value problems written by Ivo Babuška and published by . This book was released on 1975 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed-hybrid finite element approximations are described for second-order elliptic boundary-value problems in which independent approximations are used for the solution and its gradient on the interior of an element and the trace of the gradients on the boundary of the element. This leads to nonconforming finite elements. The independent boundary approximations are introduced by means of Lagrange multipliers. A-priori error estimates are derived. several other finite element models are also obtained as special cases. (Author).
Download or read book Finite Difference Methods on Irregular Networks written by Bernd Heinrich and published by Birkhauser. This book was released on 1987 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite difference and finite element methods are powerful tools for the approximate solution of differential equations governing diverse physical phenomena, and there is extensive literature on these discre tization methods. In the last two decades, some extensions of the finite difference method to irregular networks have been described and applied to solving boundary value problems in science and engineering. For instance, "box integration methods" have been widely used in electro nics. There are several papers on this topic, but a comprehensive study of these methods does not seem to have been attempted. The purpose of this book is to provide a systematic treatment of a generalized finite difference method on irregular networks for solving numerically elliptic boundary value problems. Thus, several disadvan tages of the classical finite difference method can be removed, irregular networks of triangles known from the finite element method can be applied, and advantageous properties of the finite difference approxima tions will be obtained. The book is written for advanced undergraduates and graduates in the area of numerical analysis as well as for mathematically inclined workers in engineering and science. In preparing the material for this book, the author has greatly benefited from discussions and collaboration with many colleagues who are concerned with finite difference or (and) finite element methods.
Download or read book Large Scale Scientific Computing written by Ivan Lirkov and published by Springer. This book was released on 2004-01-30 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume were presented at the 4th International Conference on Large-Scale Scientific Computations ICLSSC 2003. It was held in Sozopol, Bulgaria, June 4-8, 2003. The conference was organized and sponsored by the Central Laboratory for Parallel Processing at the Bulgarian Academy of Sciences. Support was also provided from the Center of Excellence "BIS 21" (funded by the European Commission), SIAM and GAMM. A co-organizer of this traditional scientific meeting was the Division of Numerical Analysis and Statistics of the University of Rousse. The success of the conference and the present volume in particular are the outcome of the joint efforts of many colleagues from various institutions and organizations. First thanks to all the members of the Scientific Committee for their valuable contribution to forming the scientific face of the conference, as well as for their help in reviewing contributed papers. We would like to specially thank the organizers of the special sessions: R. Blaheta, N. Dimitrova, A. Ebel, K. Georgiev, O. Iliev, A. Karaivanova, H. Kosina, M. Krastanov, U. Langer, P. Minev, M. Neytcheva, M. Sch ̈ afer, V. Veliov, and Z. Zlatev. We are also grateful to the staff involved in the local organization. Special Events: - The conference was devoted to the 60th anniversary of Raytcho Lazarov. - During the conference, the nomination for the World Level of the Hall of Fame for Engineering, Science and Technology, HOFEST, was officially awarded to Owe Axelsson.
Download or read book Numerical Methods and Applications written by Ivan Lirkov and published by Springer Science & Business Media. This book was released on 2003 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Numerical Methods and Applications written by Ivan Tomov Dimov and published by World Scientific. This book was released on 1994 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances In Numerical Methods And Applications Ii Proceedings Of The Fourth International Conference written by Panayot S Vassilevski and published by World Scientific. This book was released on 1999-07-05 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications.
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
