Download or read book On the Rate of Convergence of the Nonlinear Galerkin Methods written by Christophe Devulder and published by . This book was released on 1991 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Convergence of Optimum Nonlinear Galerkin Method written by He (Yinnian.) and published by . This book was released on 1997 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Two Point Boundary Value Problems Lower and Upper Solutions written by C. De Coster and published by Elsevier. This book was released on 2006-03-21 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Download or read book Computational Galerkin Methods written by C. A. J. Fletcher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the wake of the computer revolution, a large number of apparently uncon nected computational techniques have emerged. Also, particular methods have assumed prominent positions in certain areas of application. Finite element methods, for example, are used almost exclusively for solving structural problems; spectral methods are becoming the preferred approach to global atmospheric modelling and weather prediction; and the use of finite difference methods is nearly universal in predicting the flow around aircraft wings and fuselages. These apparently unrelated techniques are firmly entrenched in computer codes used every day by practicing scientists and engineers. Many of these scientists and engineers have been drawn into the computational area without the benefit offormal computational training. Often the formal computational training we do provide reinforces the arbitrary divisions between the various computational methods available. One of the purposes of this monograph is to show that many computational techniques are, indeed, closely related. The Galerkin formulation, which is being used in many subject areas, provides the connection. Within the Galerkin frame-work we can generate finite element, finite difference, and spectral methods.
Download or read book Numerical Analysis written by Andrew R. Mitchell and published by World Scientific. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.
Download or read book Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters written by H.G. Kaper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.
Download or read book Von Karman Evolution Equations written by Igor Chueshov and published by Springer Science & Business Media. This book was released on 2010-04-08 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of mathematical models that arise in the context of concrete - plications, the following two questions are of fundamental importance: (i) we- posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions. A positive answer to the ?rst question, - ing of prime interest on purely mathematical grounds, also provides an important test of the viability of the model as a description of a given physical phenomenon. An answer or insight to the second question provides a wealth of information about the model, hence about the process it describes. Of particular interest are questions related to long-time behavior of solutions. Such an evolution property cannot be v- i?ed empirically, thus any in a-priori information about the long-time asymptotics can be used in predicting an ultimate long-time response and dynamical behavior of solutions. In recent years, this set of investigations has attracted a great deal of attention. Consequent efforts have then resulted in the creation and infusion of new methods and new tools that have been responsible for carrying out a successful an- ysis of long-time behavior of several classes of nonlinear PDEs.
Download or read book Stochastic Parameterizing Manifolds and Non Markovian Reduced Equations written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-23 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Download or read book An Introduction to Element Based Galerkin Methods on Tensor Product Bases written by Francis X. Giraldo and published by Springer Nature. This book was released on 2020-10-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.
Download or read book Approximate Solution of Operator Equations written by M.A. Krasnosel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Download or read book Methods of Accelerated Convergence in Nonlinear Mechanics written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by . This book was released on 1976 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Procedures in Nonlinear Oscillation Theory written by Nikolai A. Bobylev and published by Walter de Gruyter. This book was released on 2012-05-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018) Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Local Discontinuous Galerkin Method for Time Dependent Convection Diffusion Systems written by Bernardo Cockburn and published by . This book was released on 1997 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the Local Discontinuous Galerkin methods for non-linear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.
Download or read book Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis written by Society for Industrial and Applied Mathematics and published by . This book was released on 2004 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
