Compatible Spatial Discretizations

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Compatible Spatial Discretizations

Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov
Compatible Spatial Discretizations Book PDF

Author : Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 46,8 Mb
Release : 2007-01-26
Category : Mathematics
ISBN : 9780387380346

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Compatible Spatial Discretizations by Douglas N. Arnold,Pavel B. Bochev,Richard B. Lehoucq,Roy A. Nicolaides,Mikhail Shashkov Pdf

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.

IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs

Annalisa Buffa,Giancarlo Sangalli
IsoGeometric Analysis A New Paradigm in the Numerical Approximation of PDEs Book PDF

Author : Annalisa Buffa,Giancarlo Sangalli
Publisher : Springer
Page : 193 pages
File Size : 43,6 Mb
Release : 2016-10-05
Category : Mathematics
ISBN : 9783319423098

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IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs by Annalisa Buffa,Giancarlo Sangalli Pdf

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow. The contributions were written by Carla Manni and Hendrik Speelers, Vibeke Skytt and Tor Dokken, Lourenco Beirao da Veiga, Annalisa Buffa, Giancarlo Sangalli and Rafael Vazquez, and finally by John Evans and Thomas J.R. Hughes.

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 : 45,5 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.

Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems

Clément Cancès,Pascal Omnes
Finite Volumes for Complex Applications VIII Hyperbolic Elliptic and Parabolic Problems Book PDF

Author : Clément Cancès,Pascal Omnes
Publisher : Springer
Page : 559 pages
File Size : 52,7 Mb
Release : 2017-05-22
Category : Mathematics
ISBN : 9783319573946

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Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems by Clément Cancès,Pascal Omnes Pdf

This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete l evel. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is useful for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.

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 : 44,5 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

Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems

Christoph Lohmann
Physics Compatible Finite Element Methods for Scalar and Tensorial Advection Problems Book PDF

Author : Christoph Lohmann
Publisher : Springer Nature
Page : 283 pages
File Size : 46,8 Mb
Release : 2019-10-14
Category : Mathematics
ISBN : 9783658277376

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Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems by Christoph Lohmann Pdf

Christoph Lohmann introduces a very general framework for the analysis and design of bound-preserving finite element methods. The results of his in-depth theoretical investigations lead to promising new extensions and modifications of existing algebraic flux correction schemes. The main focus is on new limiting techniques designed to control the range of solution values for advected scalar quantities or the eigenvalue range of symmetric tensors. The author performs a detailed case study for the Folgar-Tucker model of fiber orientation dynamics. Using eigenvalue range preserving limiters and admissible closure approximations, he develops a physics-compatible numerical algorithm for this model.

Numerical Mathematics and Advanced Applications

Alfredo Bermúdez de Castro,Dolores Gómez,Peregrina Quintela,Pilar Salgado
Numerical Mathematics and Advanced Applications Book PDF

Author : Alfredo Bermúdez de Castro,Dolores Gómez,Peregrina Quintela,Pilar Salgado
Publisher : Springer Science & Business Media
Page : 1202 pages
File Size : 51,5 Mb
Release : 2007-10-08
Category : Mathematics
ISBN : 9783540342885

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Numerical Mathematics and Advanced Applications by Alfredo Bermúdez de Castro,Dolores Gómez,Peregrina Quintela,Pilar Salgado Pdf

These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

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 : 42,6 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 Mathematics and Advanced Applications ENUMATH 2019

Fred J. Vermolen,Cornelis Vuik
Numerical Mathematics and Advanced Applications ENUMATH 2019 Book PDF

Author : Fred J. Vermolen,Cornelis Vuik
Publisher : Springer Nature
Page : 1185 pages
File Size : 46,6 Mb
Release : 2021-04-30
Category : Mathematics
ISBN : 9783030558741

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Numerical Mathematics and Advanced Applications ENUMATH 2019 by Fred J. Vermolen,Cornelis Vuik Pdf

This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 Book PDF

Author : Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Publisher : Springer Nature
Page : 658 pages
File Size : 41,7 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9783030396473

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 by Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab Pdf

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, 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.

Acta Numerica 2006: Volume 15

Arieh Iserles
Acta Numerica 2006 Volume 15 Book PDF

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 658 pages
File Size : 53,5 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 0521868157

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Acta Numerica 2006: Volume 15 by Arieh Iserles Pdf

A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Mimetic Discretization Methods

Jose E. Castillo,Guillermo F. Miranda
Mimetic Discretization Methods Book PDF

Author : Jose E. Castillo,Guillermo F. Miranda
Publisher : CRC Press
Page : 256 pages
File Size : 45,7 Mb
Release : 2013-01-10
Category : Mathematics
ISBN : 9781466513440

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Mimetic Discretization Methods by Jose E. Castillo,Guillermo F. Miranda Pdf

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and flux-integral operators, enabling the same order of accuracy in the interior as well as the domain boundary. After an overview of various mimetic approaches and applications, the text discusses the use of continuum mathematical models as a way to motivate the natural use of mimetic methods. The authors also offer basic numerical analysis material, making the book suitable for a course on numerical methods for solving PDEs. The authors cover mimetic differential operators in one, two, and three dimensions and provide a thorough introduction to object-oriented programming and C++. In addition, they describe how their mimetic methods toolkit (MTK)-available online-can be used for the computational implementation of mimetic discretization methods. The text concludes with the application of mimetic methods to structured nonuniform meshes as well as several case studies. Compiling the authors' many concepts and results developed over the years, this book shows how to obtain a robust numerical solution of PDEs using the mimetic discretization approach. It also helps readers compare alternative methods in the literature.

Isogeometric Analysis and Applications 2018

Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler
Isogeometric Analysis and Applications 2018 Book PDF

Author : Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler
Publisher : Springer Nature
Page : 279 pages
File Size : 53,8 Mb
Release : 2021-01-13
Category : Mathematics
ISBN : 9783030498368

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Isogeometric Analysis and Applications 2018 by Harald van Brummelen,Cornelis Vuik,Matthias Möller,Clemens Verhoosel,Bernd Simeon,Bert Jüttler Pdf

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018. This conference series, previously held in Linz, Austria, in 2012 and Annweiler am Trifels, Germany, in 2014, has created an international forum for interaction between scientists and practitioners working in this rapidly developing field. Isogeometric analysis is a groundbreaking computational approach that aims to bridge the gap between numerical analysis and computational geometry modeling by integrating the finite element method and related numerical simulation techniques into the computer-aided design workflow, and vice versa. The methodology has matured over the last decade both in terms of our theoretical understanding, its mathematical foundation and the robustness and efficiency of its practical implementations. This development has enabled scientists and practitioners to tackle challenging new applications at the frontiers of research in science and engineering and attracted early adopters for this his novel computer-aided design and engineering technology in industry. The IGAA 2018 conference brought together experts on isogeometric analysis theory and application, share their insights into challenging industrial applications and to discuss the latest developments as well as the directions of future research and development that are required to make isogeometric analysis an established mainstream technology.

Numerical Methods for PDEs

Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Numerical Methods for PDEs Book PDF

Author : Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Publisher : Springer
Page : 312 pages
File Size : 43,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319946764

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Numerical Methods for PDEs by Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia Pdf

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

ICIAM 07

Rolf Jeltsch
ICIAM 07 Book PDF

Author : Rolf Jeltsch
Publisher : European Mathematical Society
Page : 528 pages
File Size : 53,5 Mb
Release : 2009
Category : Mathematics
ISBN : 3037190566

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ICIAM 07 by Rolf Jeltsch Pdf

The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organization of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The Sixth ICIAM Congress was held in Zurich, Switzerland, July 16-20, 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congress, the appreciations of the ICIAM Prize winners' achievements, and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers in their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives, and open problems. Topics embrace analysis of and numerical methods for: linear and nonlinear partial differential equations multiscale modeling nonlinear problems involving integral operators controllability and observability asymptotic solutions of Hamilton-Jacobi equations contact problems in solid mechanics topology optimization of structures dissipation inequalities in systems theory greedy algorithms sampling in function space order-value optimization parabolic partial differential equations and deterministic games Moreover, particular applications involve risk in financial markets, radar imaging, brain dynamics, and complex geometric optics applied to acoustics and electromagnetics.