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Mixed Finite Element Methods and Applications

Mixed Finite Element Methods and Applications Author Daniele Boffi
ISBN-10 9783642365195
Release 2013-07-02
Pages 685
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Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.



A Simple Introduction to the Mixed Finite Element Method

A Simple Introduction to the Mixed Finite Element Method Author Gabriel N. Gatica
ISBN-10 9783319036953
Release 2014-01-09
Pages 132
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The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.



Finite Element Methods for Incompressible Flow Problems

Finite Element Methods for Incompressible Flow Problems Author Volker John
ISBN-10 9783319457505
Release 2016-10-27
Pages 812
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This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.



Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 Author Marco L. Bittencourt
ISBN-10 9783319658704
Release 2017-12-06
Pages 700
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This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.



Computational Electromagnetism

Computational Electromagnetism Author Houssem Haddar
ISBN-10 9783319193069
Release 2015-07-20
Pages 240
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Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.



The Finite Element Method Theory Implementation and Applications

The Finite Element Method  Theory  Implementation  and Applications Author Mats G. Larson
ISBN-10 9783642332876
Release 2013-01-13
Pages 395
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This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​



Mixed and Hybrid Finite Element Methods

Mixed and Hybrid Finite Element Methods Author Franco Brezzi
ISBN-10 9781461231721
Release 2012-12-06
Pages 350
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Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.



Advances in Discretization Methods

Advances in Discretization Methods Author Giulio Ventura
ISBN-10 9783319412467
Release 2016-08-24
Pages 269
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This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.



Compatible Spatial Discretizations

Compatible Spatial Discretizations Author Douglas N. Arnold
ISBN-10 9780387380346
Release 2007-01-26
Pages 247
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The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.



Numerical Solution of Partial Differential Equations Theory Algorithms and Their Applications

Numerical Solution of Partial Differential Equations  Theory  Algorithms  and Their Applications Author Oleg P. Iliev
ISBN-10 9781461471721
Release 2013-06-04
Pages 327
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One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.



Finite Element Methods with B Splines

Finite Element Methods with B Splines Author Klaus Hollig
ISBN-10 9780898716993
Release 2012-12-13
Pages 156
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An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.



Journal of the Korean Mathematical Society

Journal of the Korean Mathematical Society Author
ISBN-10 UOM:39015072605549
Release 2007
Pages
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Journal of the Korean Mathematical Society has been writing in one form or another for most of life. You can find so many inspiration from Journal of the Korean Mathematical Society also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Journal of the Korean Mathematical Society book for free.



The Least Squares Finite Element Method

The Least Squares Finite Element Method Author Bo-nan Jiang
ISBN-10 3540639349
Release 1998-06-22
Pages 418
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Here is a comprehensive introduction to the least-squares finite element method (LSFEM) for numerical solution of PDEs. It covers the theory for first-order systems, particularly the div-curl and the div-curl-grad system. Then LSFEM is applied systematically to permissible boundary conditions for the incompressible Navier-Stokes equations, to show that the divergence equations in the Maxwell equations are not redundant, and to derive equivalent second-order versions of the Navier-Stokes equations and the Maxwell equations. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics, including incompressible viscous flows, rotational inviscid flows, low-Mach-number compressible flows, two-fluid and convective flows, scattering waves, etc.



Topics in Computational Wave Propagation

Topics in Computational Wave Propagation Author Mark Ainsworth
ISBN-10 9783642554834
Release 2012-12-06
Pages 410
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These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.



Advanced Finite Element Technologies

Advanced Finite Element Technologies Author Jörg Schröder
ISBN-10 9783319319254
Release 2016-05-19
Pages 236
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The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.



RAIRO

RAIRO Author EDP Sciences
ISBN-10 UOM:39015072634507
Release 2008
Pages
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RAIRO has been writing in one form or another for most of life. You can find so many inspiration from RAIRO also informative, and entertaining. Click DOWNLOAD or Read Online button to get full RAIRO book for free.



Multiscale and Adaptivity Modeling Numerics and Applications

Multiscale and Adaptivity  Modeling  Numerics and Applications Author Silvia Bertoluzza
ISBN-10 9783642240782
Release 2012-01-07
Pages 314
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This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.