The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems
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The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems
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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher: Independently Published
Release Date : 2018-10-15
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems written by National Aeronautics and Space Adm Nasa and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-15 with Science categories.
In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown. Cockburn, Bernardo and Shu, Chi-Wang Langley Research Center NAS1-19480; DAAH04-94-G-0205; NSF DMS-94-00814; NSF DMS-94-07952; NAG1-1145; AF-AFOSR-95-1-0074; RTOP 505-90-52-01
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems
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Author : Bernardo Cockburn
language : en
Publisher:
Release Date : 1997
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems written by Bernardo Cockburn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Discontinuous Galerkin Methods
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Author : Bernardo Cockburn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discontinuous Galerkin Methods written by Bernardo Cockburn 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 2012-12-06 with Mathematics categories.
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.
Third Order Maximum Principle Satisfying Direct Discontinuous Galerkin Methods For Time Dependent Convection Diffusion Equations On Unstructured Triangular Meshes
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Author :
language : en
Publisher:
Release Date : 2015
Third Order Maximum Principle Satisfying Direct Discontinuous Galerkin Methods For Time Dependent Convection Diffusion Equations On Unstructured Triangular Meshes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair ([beta]0, [beta]1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.
Computational Fluid And Solid Mechanics 2003
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Author : K.J Bathe
language : en
Publisher: Elsevier
Release Date : 2003-06-02
Computational Fluid And Solid Mechanics 2003 written by K.J Bathe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-02 with Science categories.
Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis
Nonlinear Diffusion Problems
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Author : O. Diekmann
language : en
Publisher:
Release Date : 1976
Nonlinear Diffusion Problems written by O. Diekmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Differential equations, Nonlinear categories.
Analytical And Numerical Methods For Volterra Equations
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Author : Peter Linz
language : en
Publisher: SIAM
Release Date : 1985-01-01
Analytical And Numerical Methods For Volterra Equations written by Peter Linz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Runge Kutta Discontinuous Galerkin Methods For Convection Dominated Problems
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Author : Bernardo Cockburn
language : en
Publisher:
Release Date : 2000
Runge Kutta Discontinuous Galerkin Methods For Convection Dominated Problems written by Bernardo Cockburn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
High Order Methods For Computational Physics
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Author : Timothy J. Barth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
High Order Methods For Computational Physics written by Timothy J. Barth 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 2013-03-09 with Mathematics categories.
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Galerkin Finite Element Methods For Parabolic Problems
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Author : Vidar Thomee
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Galerkin Finite Element Methods For Parabolic Problems written by Vidar Thomee 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 2013-04-17 with Mathematics categories.
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.