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The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

2018-10-15 Science
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Release : 2018-10-15
Genre : Science
Kind : eBook
Book Rating : 626/5 ( reviews)

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Book Synopsis The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems by : National Aeronautics and Space Adm Nasa

Download or read book The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems written by National Aeronautics and Space Adm Nasa. This book was released on 2018-10-15. Available in PDF, EPUB and Kindle. Book excerpt: 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

1997
Download The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems PDF Online Free

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Release : 1997
Genre :
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Book Synopsis The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems by : Bernardo Cockburn

Download or read book The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems written by Bernardo Cockburn. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the Local Discontinuous Galerkin methods for non-linear, 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 L2-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.

Discontinuous Galerkin Methods

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 211/5 ( reviews)

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Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn

Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn. This book was released on 2012-12-06. 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.

Discontinuous Galerkin Method

2015-07-17 Mathematics
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Release : 2015-07-17
Genre : Mathematics
Kind : eBook
Book Rating : 671/5 ( reviews)

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Book Synopsis Discontinuous Galerkin Method by : Vít Dolejší

Download or read book Discontinuous Galerkin Method written by Vít Dolejší. This book was released on 2015-07-17. 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.

The Local Discontinuous Galerkin Method for Time-dependent Convection-diffusion Systems

1997
Download The Local Discontinuous Galerkin Method for Time-dependent Convection-diffusion Systems PDF Online Free

Author :
Release : 1997
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis The Local Discontinuous Galerkin Method for Time-dependent Convection-diffusion Systems by : Bernardo Cockburn

Download or read book The Local Discontinuous Galerkin Method for Time-dependent Convection-diffusion Systems written by Bernardo Cockburn. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt:

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