Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Analysis And Applications Of Discontinuous Galerkin Methods For Hyperbolic Equations PDF full book. Access full book title Analysis And Applications Of Discontinuous Galerkin Methods For Hyperbolic Equations.
| Author | : He Yang |
| Publisher | : |
| Total Pages | : 310 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
| Author | : Bernardo Cockburn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642597211 |
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 | : Remi Abgrall |
| Publisher | : Elsevier |
| Total Pages | : 612 |
| Release | : 2017-01-16 |
| Genre | : Mathematics |
| ISBN | : 044463911X |
Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
| Author | : Giuseppe Geymonat |
| Publisher | : World Scientific |
| Total Pages | : 196 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 9789971502058 |
This book introduces the general aspects of hyperbolic conservation laws and their numerical approximation using some of the most modern tools: spectral methods, unstructured meshes and ?-formulation. The applications of these methods are found in some significant examples such as the Euler equations. This book, a collection of articles by the best authors in the field, exposes the reader to the frontier of the research and many open problems.
| Author | : Claes Johnson |
| Publisher | : |
| Total Pages | : 62 |
| Release | : 1984 |
| Genre | : Differential equations, Hyperbolic |
| ISBN | : 9789517531511 |
| Author | : Timothy J. Barth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 594 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 366203882X |
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.
| Author | : Xiaobing Feng |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 289 |
| Release | : 2013-11-08 |
| Genre | : Mathematics |
| ISBN | : 3319018183 |
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
| Author | : Remi Abgrall |
| Publisher | : Elsevier |
| Total Pages | : 668 |
| Release | : 2016-11-17 |
| Genre | : Mathematics |
| ISBN | : 0444637958 |
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage
| Author | : Sirvan Rahmati |
| Publisher | : |
| Total Pages | : 60 |
| Release | : 2020 |
| Genre | : Electronic dissertations |
| ISBN | : |
This thesis is concerned with the investigation of the superconvergence of the Discontinuous Method for linear conservation laws. We use Fourier analysis to study the superconvergence of the semi-discrete discontinuous Galerkin method for scalar linear advection equations in one spatial dimension. We provide the error bounds and asymptotic errors for initial di erent initial discretizations. For the pedagogical purpose, the errors are computed in two di erent ways. In the rst approach, we compute the di erence between the numerical solution and a special interpolation of the exact solution, and show that it consists of an asymptotic error of order 2k + 1 (where k is the order of polynomial approximation) and a transient error of lower order. In the second approach, we compute the error directly by decomposing it into physical and nonphysical modes, and obtain agreement with the rst approach. We then extend the analysis to vector conservation laws, solved using the Lax-Friedrichs ux. We prove that the superconvergence holds with the same order. The error bounds and asymptotic errors are demonstrated by various numerical experiments for scalar and vector advection equations.
| Author | : Francis X. Giraldo |
| Publisher | : Springer Nature |
| Total Pages | : 559 |
| Release | : 2020-10-30 |
| Genre | : Mathematics |
| ISBN | : 3030550699 |
This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.
