Mixed Finite Elements Compatibility Conditions And Applications

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Mixed Finite Elements, Compatibility Conditions, and Applications

Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Mixed Finite Elements Compatibility Conditions and Applications Book PDF

Author : Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 50,9 Mb
Release : 2008-04-14
Category : Mathematics
ISBN : 9783540783145

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Mixed Finite Elements, Compatibility Conditions, and Applications by Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Mixed Finite Elements, Compatibility Conditions, and Applications

Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Mixed Finite Elements Compatibility Conditions and Applications Book PDF

Author : Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Unknown
Page : 235 pages
File Size : 45,7 Mb
Release : 2008
Category : Differential equations, Partial
ISBN : OCLC:1035662841

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Mixed Finite Elements, Compatibility Conditions, and Applications by Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Mixed Finite Elements, Compatibility Conditions, and Applications

Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Mixed Finite Elements Compatibility Conditions and Applications Book PDF

Author : Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin
Publisher : Springer
Page : 244 pages
File Size : 46,5 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 3540847634

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Mixed Finite Elements, Compatibility Conditions, and Applications by Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin Pdf

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Numerical Mathematics and Advanced Applications - ENUMATH 2013

Assyr Abdulle,Simone Deparis,Daniel Kressner,Fabio Nobile,Marco Picasso
Numerical Mathematics and Advanced Applications ENUMATH 2013 Book PDF

Author : Assyr Abdulle,Simone Deparis,Daniel Kressner,Fabio Nobile,Marco Picasso
Publisher : Springer
Page : 810 pages
File Size : 54,9 Mb
Release : 2014-11-25
Category : Computers
ISBN : 9783319107059

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Numerical Mathematics and Advanced Applications - ENUMATH 2013 by Assyr Abdulle,Simone Deparis,Daniel Kressner,Fabio Nobile,Marco Picasso Pdf

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

Numerical Mathematics and Advanced Applications ENUMATH 2015

Bülent Karasözen,Murat Manguoğlu,Münevver Tezer-Sezgin,Serdar Göktepe,Ömür Uğur
Numerical Mathematics and Advanced Applications ENUMATH 2015 Book PDF

Author : Bülent Karasözen,Murat Manguoğlu,Münevver Tezer-Sezgin,Serdar Göktepe,Ömür Uğur
Publisher : Springer
Page : 643 pages
File Size : 48,7 Mb
Release : 2016-11-09
Category : Mathematics
ISBN : 9783319399294

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Numerical Mathematics and Advanced Applications ENUMATH 2015 by Bülent Karasözen,Murat Manguoğlu,Münevver Tezer-Sezgin,Serdar Göktepe,Ömür Uğur Pdf

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.

Geometrically Unfitted Finite Element Methods and Applications

Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Geometrically Unfitted Finite Element Methods and Applications Book PDF

Author : Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Publisher : Springer
Page : 361 pages
File Size : 44,6 Mb
Release : 2018-03-13
Category : Mathematics
ISBN : 9783319714318

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Geometrically Unfitted Finite Element Methods and Applications by Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii Pdf

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.

Computing with hp-ADAPTIVE FINITE ELEMENTS

Leszek Demkowicz,Jason Kurtz,David Pardo,Maciek Paszenski,Waldemar Rachowicz,Adam Zdunek
Computing with hp ADAPTIVE FINITE ELEMENTS Book PDF

Author : Leszek Demkowicz,Jason Kurtz,David Pardo,Maciek Paszenski,Waldemar Rachowicz,Adam Zdunek
Publisher : CRC Press
Page : 437 pages
File Size : 44,9 Mb
Release : 2007-11-02
Category : Mathematics
ISBN : 9781420011692

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Computing with hp-ADAPTIVE FINITE ELEMENTS by Leszek Demkowicz,Jason Kurtz,David Pardo,Maciek Paszenski,Waldemar Rachowicz,Adam Zdunek Pdf

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the

Hybrid and Incompatible Finite Element Methods

Theodore H.H. Pian,Chang-Chun Wu
Hybrid and Incompatible Finite Element Methods Book PDF

Author : Theodore H.H. Pian,Chang-Chun Wu
Publisher : CRC Press
Page : 395 pages
File Size : 45,7 Mb
Release : 2005-11-04
Category : Mathematics
ISBN : 9781135442217

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Hybrid and Incompatible Finite Element Methods by Theodore H.H. Pian,Chang-Chun Wu Pdf

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

Mixed Finite Element Methods and Applications

Daniele Boffi,Franco Brezzi,Michel Fortin
Mixed Finite Element Methods and Applications Book PDF

Author : Daniele Boffi,Franco Brezzi,Michel Fortin
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 42,7 Mb
Release : 2013-07-02
Category : Mathematics
ISBN : 9783642365195

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Mixed Finite Element Methods and Applications by Daniele Boffi,Franco Brezzi,Michel Fortin Pdf

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.

Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods

David Pardo,Paweł J. Matuszyk,Vladimir Puzyrev,Carlos Torres-Verdin,Myung Jin Nam,Victor M. Calo
Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods Book PDF

Author : David Pardo,Paweł J. Matuszyk,Vladimir Puzyrev,Carlos Torres-Verdin,Myung Jin Nam,Victor M. Calo
Publisher : Elsevier
Page : 314 pages
File Size : 50,7 Mb
Release : 2021-05-22
Category : Science
ISBN : 9780128214657

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Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods by David Pardo,Paweł J. Matuszyk,Vladimir Puzyrev,Carlos Torres-Verdin,Myung Jin Nam,Victor M. Calo Pdf

Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods provides a comprehensive review of different resistivity and sonic logging instruments used within the oil industry, along with precise and solid mathematical descriptions of the physical equations and corresponding FE formulations that govern these measurements. Additionally, the book emphasizes the main modeling considerations that one needs to incorporate into the simulations in order to obtain reliable and accurate results. Essentially, the formulations and methods described here can also be applied to simulate on-surface geophysical measurements such as seismic or marine controlled-source electromagnetic (CSEM) measurements. Simulation results obtained using FE methods are superior. FE methods employ a mathematical terminology based on FE spaces that facilitate the design of sophisticated formulations and implementations according to the specifics of each problem. This mathematical FE framework provides a highly accurate, robust, and flexible unified environment for the solution of multi-physics problems. Thus, readers will benefit from this resource by learning how to make a variety of logging simulations using a unified FE framework. Provides a complete and unified finite element approach to perform borehole sonic and electromagnetic simulations Includes the latest research in mathematical and implementation content on Finite Element simulations of borehole logging measurements Features a variety of unique simulations and numerical examples that allow the reader to easily learn the main features and limitations that appear when simulating borehole resistivity measurements

Advanced Finite Element Methods with Applications

Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Advanced Finite Element Methods with Applications Book PDF

Author : Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publisher : Springer
Page : 428 pages
File Size : 42,9 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030142445

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Advanced Finite Element Methods with Applications by Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach Pdf

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

75 Years of Mathematics of Computation

Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
75 Years of Mathematics of Computation Book PDF

Author : Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 53,5 Mb
Release : 2020-07-29
Category : Education
ISBN : 9781470451639

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75 Years of Mathematics of Computation by Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld Pdf

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

The Gradient Discretisation Method

Jérôme Droniou,Robert Eymard,Thierry Gallouët,Cindy Guichard,Raphaèle Herbin
The Gradient Discretisation Method Book PDF

Author : Jérôme Droniou,Robert Eymard,Thierry Gallouët,Cindy Guichard,Raphaèle Herbin
Publisher : Springer
Page : 497 pages
File Size : 51,6 Mb
Release : 2018-07-31
Category : Mathematics
ISBN : 9783319790428

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The Gradient Discretisation Method by Jérôme Droniou,Robert Eymard,Thierry Gallouët,Cindy Guichard,Raphaèle Herbin Pdf

This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p

The Mimetic Finite Difference Method for Elliptic Problems

Lourenco Beirao da Veiga,Konstantin Lipnikov,Gianmarco Manzini
The Mimetic Finite Difference Method for Elliptic Problems Book PDF

Author : Lourenco Beirao da Veiga,Konstantin Lipnikov,Gianmarco Manzini
Publisher : Springer
Page : 399 pages
File Size : 43,5 Mb
Release : 2014-05-22
Category : Mathematics
ISBN : 9783319026633

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The Mimetic Finite Difference Method for Elliptic Problems by Lourenco Beirao da Veiga,Konstantin Lipnikov,Gianmarco Manzini Pdf

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

Numerical Methods and Analysis of Multiscale Problems

Alexandre L. Madureira
Numerical Methods and Analysis of Multiscale Problems Book PDF

Author : Alexandre L. Madureira
Publisher : Springer
Page : 123 pages
File Size : 48,7 Mb
Release : 2017-02-15
Category : Mathematics
ISBN : 9783319508665

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Numerical Methods and Analysis of Multiscale Problems by Alexandre L. Madureira Pdf

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.