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Author : Christian Waluga
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (794 download)
Download or read book Analysis of Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems written by Christian Waluga and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vít Dolejší
Publisher : Springer
ISBN 13 : 3319192671
Total Pages : 575 pages
Book Rating : 4.3/5 (191 download)
Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Author : Laura De Lorenzis
Publisher : Springer Nature
ISBN 13 : 3030375188
Total Pages : 225 pages
Book Rating : 4.0/5 (33 download)
Download or read book Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids written by Laura De Lorenzis and published by Springer Nature. This book was released on 2020-02-08 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.
Author : Shukai Du
Publisher : Springer Nature
ISBN 13 : 3030272303
Total Pages : 124 pages
Book Rating : 4.0/5 (32 download)
Download or read book An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method written by Shukai Du and published by Springer Nature. This book was released on 2019-08-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
Author : Jean Donea
Publisher : John Wiley & Sons
ISBN 13 : 9780471496663
Total Pages : 366 pages
Book Rating : 4.4/5 (966 download)
Download or read book Finite Element Methods for Flow Problems written by Jean Donea and published by John Wiley & Sons. This book was released on 2003-06-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Author : Volker John
Publisher : Springer
ISBN 13 : 3319457500
Total Pages : 816 pages
Book Rating : 4.3/5 (194 download)
Download or read book Finite Element Methods for Incompressible Flow Problems written by Volker John and published by Springer. This book was released on 2016-10-27 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nathan Vanderkooy Roberts
Publisher :
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.:/5 (857 download)
Download or read book A Discontinuous Petrov-Galerkin Methodology for Incompressible Flow Problems written by Nathan Vanderkooy Roberts and published by . This book was released on 2013 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incompressible flows -- flows in which variations in the density of a fluid are negligible -- arise in a wide variety of applications, from hydraulics to aerodynamics. The incompressible Navier-Stokes equations which govern such flows are also of fundamental physical and mathematical interest. They are believed to hold the key to understanding turbulent phenomena; precise conditions for the existence and uniqueness of solutions remain unknown -- and establishing such conditions is the subject of one of the Clay Mathematics Institute's Millennium Prize Problems. Typical solutions of incompressible flow problems involve both fine- and large-scale phenomena, so that a uniform finite element mesh of sufficient granularity will at best be wasteful of computational resources, and at worst be infeasible because of resource limitations. Thus adaptive mesh refinements are required. In industry, the adaptivity schemes used are ad hoc, requiring a domain expert to predict features of the solution. A badly chosen mesh may cause the code to take considerably longer to converge, or fail to converge altogether. Typically, the Navier-Stokes solve will be just one component in an optimization loop, which means that any failure requiring human intervention is costly. Therefore, I pursue technological foundations for a solver of the incompressible Navier-Stokes equations that provides robust adaptivity starting with a coarse mesh. By robust, I mean both that the solver always converges to a solution in predictable time, and that the adaptive scheme is independent of the problem -- no special expertise is required for adaptivity. The cornerstone of my approach is the discontinuous Petrov-Galerkin (DPG) finite element methodology developed by Leszek Demkowicz and Jay Gopalakrishnan. For a large class of problems, DPG can be shown to converge at optimal rates. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. Several approximations to Navier-Stokes are of interest, and I study each of these in turn, culminating in the study of the steady 2D incompressible Navier-Stokes equations. The Stokes equations can be obtained by neglecting the convective term; these are accurate for "creeping" viscous flows. The Oseen equations replace the convective term, which is nonlinear, with a linear approximation. The steady-state incompressible Navier-Stokes equations approximate the transient equations by neglecting time variations. Crucial to this work is Camellia, a toolbox I developed for solving DPG problems which uses the Trilinos numerical libraries. Camellia supports 2D meshes of triangles and quads of variable polynomial order, allows simple specification of variational forms, supports h- and p-refinements, and distributes the computation of the stiffness matrix, among other features. The central contribution of this dissertation is design and development of mathematical techniques and software, based on the DPG method, for solving the 2D incompressible Navier-Stokes equations in the laminar regime (Reynolds numbers up to about 1000). Along the way, I investigate approximations to these equations -- the Stokes equations and the Oseen equations -- followed by the steady-state Navier-Stokes equations.
Author : Bernardo Cockburn
Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
ISBN 13 : 0387720650
Total Pages : 507 pages
Book Rating : 4.3/5 (877 download)
Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Author : G. Chavent
Publisher : Elsevier
ISBN 13 : 0080875386
Total Pages : 389 pages
Book Rating : 4.0/5 (88 download)
Download or read book Mathematical Models and Finite Elements for Reservoir Simulation written by G. Chavent and published by Elsevier. This book was released on 1986-01-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.
Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030313395
Total Pages : 694 pages
Book Rating : 4.0/5 (33 download)
Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Author : Aditya Kiran Pandare
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (91 download)
Download or read book A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin Finite Element Method for Incompressible Flows on Unstructured Grids written by Aditya Kiran Pandare and published by . This book was released on 2015 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ben Q. Li
Publisher : Springer Science & Business Media
ISBN 13 : 1846282055
Total Pages : 587 pages
Book Rating : 4.8/5 (462 download)
Download or read book Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer written by Ben Q. Li and published by Springer Science & Business Media. This book was released on 2006-06-29 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.
Author : Shukai Du
Publisher : Springer
ISBN 13 : 9783030272296
Total Pages : 124 pages
Book Rating : 4.2/5 (722 download)
Download or read book An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method written by Shukai Du and published by Springer. This book was released on 2019-09-14 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
Author : Alexandre Ern
Publisher : Springer Nature
ISBN 13 : 3030569233
Total Pages : 491 pages
Book Rating : 4.0/5 (35 download)
Download or read book Finite Elements II written by Alexandre Ern and published by Springer Nature. This book was released on 2021-04-22 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Author : Andrea Toselli
Publisher : Springer Science & Business Media
ISBN 13 : 3540266623
Total Pages : 454 pages
Book Rating : 4.5/5 (42 download)
Download or read book Domain Decomposition Methods - Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Author : Jordi Vila Pérez
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (112 download)
Download or read book HI-FI Hybridisable Discontinuous Galerkin Method for Incompressible Flows written by Jordi Vila Pérez and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing interest in high-order discretization techniques for CFD applications is motivated by the high accuracy that these methods provide compared to low-order methods. In this project, the hybridizable discontinuous Galerkin (HDG) method is discussed. HDG represents a novel and competitive alternative to the classical discontinuous Galerkin method by substantially reducing the number of coupled unknowns of the discrete problem. Some numerical examples for the simulation of steady incompressible flows are presented, with special emphasis on the HDG stabilization term in order to ensure the optimal convergence of velocity, pressure and gradient of velocity and the superconvergence of a postprocessed velocity field.
