The Mimetic Finite Difference Method For Elliptic Problems
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The Mimetic Finite Difference Method For Elliptic Problems
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Author : Lourenco Beirao da Veiga
language : en
Publisher: Springer
Release Date : 2014-05-22
The Mimetic Finite Difference Method For Elliptic Problems written by Lourenco Beirao da Veiga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with Mathematics categories.
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.
The Gradient Discretisation Method
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Author : Jérôme Droniou
language : en
Publisher: Springer
Release Date : 2018-07-31
The Gradient Discretisation Method written by Jérôme Droniou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-31 with Mathematics categories.
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
Bem Based Finite Element Approaches On Polytopal Meshes
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Author : Steffen Weißer
language : en
Publisher: Springer
Release Date : 2019-07-18
Bem Based Finite Element Approaches On Polytopal Meshes written by Steffen Weißer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Mathematics categories.
This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Numerical Mathematics And Advanced Applications Enumath 2013
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Author : Assyr Abdulle
language : en
Publisher: Springer
Release Date : 2014-11-25
Numerical Mathematics And Advanced Applications Enumath 2013 written by Assyr Abdulle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Computers categories.
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.
Finite Volumes For Complex Applications Vi Problems Perspectives
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Author : Jaroslav Fořt
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-21
Finite Volumes For Complex Applications Vi Problems Perspectives written by Jaroslav Fořt 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 2011-07-21 with Mathematics categories.
Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applications VI is to bring together mathematicians, physicists and engineers dealing with Finite Volume Techniques in a wide context. This book, divided in two volumes, brings a critical look at the subject (new ideas, limits or drawbacks of methods, theoretical as well as applied topics).
Polyhedral Methods In Geosciences
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Author : Daniele Antonio Di Pietro
language : en
Publisher: Springer Nature
Release Date : 2021-06-14
Polyhedral Methods In Geosciences written by Daniele Antonio Di Pietro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-14 with Mathematics categories.
The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge of advanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.
The Hybrid High Order Method For Polytopal Meshes
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Author : Daniele Antonio Di Pietro
language : en
Publisher: Springer Nature
Release Date : 2020-04-03
The Hybrid High Order Method For Polytopal Meshes written by Daniele Antonio Di Pietro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Mathematics categories.
This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.
Large Scale Scientific Computing
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Author : Ivan Lirkov
language : en
Publisher: Springer
Release Date : 2014-06-26
Large Scale Scientific Computing written by Ivan Lirkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Large-Scale Scientific Computations, LSSC 2013, held in Sozopol, Bulgaria, in June 2013. The 74 revised full papers presented together with 5 plenary and invited papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on numerical modeling of fluids and structures; control and uncertain systems; Monte Carlo methods: theory, applications and distributed computing; theoretical and algorithmic advances in transport problems; applications of metaheuristics to large-scale problems; modeling and numerical simulation of processes in highly heterogeneous media; large-scale models: numerical methods, parallel computations and applications; numerical solvers on many-core systems; cloud and grid computing for resource-intensive scientific applications.
Simulation Of Flow In Porous Media
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Author : Peter Bastian
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31
Simulation Of Flow In Porous Media written by Peter Bastian 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 2013-07-31 with Mathematics categories.
Subsurface flow problems are inherently multiscale in space due to the large variability of material properties and in time due to the coupling of many different physical processes, such as advection, diffusion, reaction and phase exchange. Subsurface flow models still need considerable development. For example, nonequilibrium effects, entrapped air, anomalous dispersion and hysteresis effects can still not be adequately described. Moreover, parameters of the models are diffcult to access and often uncertain. Computational issues in subsurface flows include the treatment of strong heterogeneities and anisotropies in the models, the effcient solution of transport-reaction problems with many species, treatment of multiphase-multicomponent flows and the coupling of subsurface flow models to surface flow models given by shallow water or Stokes equations. With respect to energy and the environment, in particular the modelling and simulation of radioactive waste management and sequestration of CO2 underground have gained high interest in the community in recent years. Both applications provide unique challenges ranging from modelling of clay materials to treating very large scale models with high-performance computing. This book brings together key numerical mathematicians whose interest is in the analysis and computation of multiscale subsurface flow and practitioners from engineering and industry whose interest is in the applications of these core problems.
Numerical Methods For Pdes
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Author : Daniele Antonio Di Pietro
language : en
Publisher: Springer
Release Date : 2018-10-12
Numerical Methods For Pdes written by Daniele Antonio Di Pietro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.
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.