Error Estimates For Advanced Galerkin Methods
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Error Estimates For Advanced Galerkin Methods
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Author : Marcus Olavi Rüter
language : en
Publisher: Springer Nature
Release Date : 2019-11-07
Error Estimates For Advanced Galerkin Methods written by Marcus Olavi Rüter and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-07 with Science categories.
This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.
Galerkin Finite Element Methods For Parabolic Problems
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Author : Vidar Thomee
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Galerkin Finite Element Methods For Parabolic Problems written by Vidar Thomee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Numerical Mathematics And Advanced Applications 2011
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Author : Andrea Cangiani
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-20
Numerical Mathematics And Advanced Applications 2011 written by Andrea Cangiani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-20 with Mathematics categories.
The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
A Posteriori Error Estimates For Advanced Galerkin Methods
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Author : Marcus Rüter
language : en
Publisher:
Release Date : 2017
A Posteriori Error Estimates For Advanced Galerkin Methods written by Marcus Rüter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Numerical Mathematics And Advanced Applications 2009
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Author : Gunilla Kreiss
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-19
Numerical Mathematics And Advanced Applications 2009 written by Gunilla Kreiss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with Mathematics categories.
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Computational Galerkin Methods
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Author : C. A. J. Fletcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Galerkin Methods written by C. A. J. Fletcher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Numerical Mathematics And Advanced Applications
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Author : Karl Kunisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-19
Numerical Mathematics And Advanced Applications written by Karl Kunisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-19 with Mathematics categories.
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.
Discontinuous Galerkin Methods
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Author : Bernardo Cockburn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discontinuous Galerkin Methods written by Bernardo Cockburn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2020 1
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Author : Jens M. Melenk
language : en
Publisher: Springer Nature
Release Date : 2023-06-30
Spectral And High Order Methods For Partial Differential Equations Icosahom 2020 1 written by Jens M. Melenk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-30 with Mathematics categories.
The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
A Posteriori Estimates For Partial Differential Equations
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Author : Sergey I. Repin
language : en
Publisher: Walter de Gruyter
Release Date : 2008-10-31
A Posteriori Estimates For Partial Differential Equations written by Sergey I. Repin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-31 with Mathematics categories.
This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.