Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications by

Description: Nodal Discontinuous Galerkin Methods by Jan S. Hesthaven, Tim Warburton 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 PDEs, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDEs: Maxwells equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations. Notes The text 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. This is the first text on DG-FEM, suitable both as a textbook and for self study. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEs, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEs. Attention is paid to both basic analysis and algorithmic issues. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters. Back Cover This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems. These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications. This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight. Jan S. Hesthaven is a professor of Applied Mathematics at Brown University. Tim Warburton is an assistant professor of Applied and Computational Mathematics at Rice University. Author Biography Jan Hesthaven is a Professor of Applied Mathematics at Brown University. Table of Contents The key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension. Review From the reviews:"This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering."-Mathematical Reviews"The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k)"This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008) Long Description The text 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. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEs, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEs, e.g., Maxwell?s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations. These developments are done in detail in one and two dimensions on general unstructured grids with high-order elements and all essential routines for 3D extensions are also included and discussed briefly. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters. Review Quote From the reviews:"This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering."-Mathematical Reviews"The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k)"This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008) Feature First text on DG-FEM, suitable both as a textbook and for self sudy Attention to both basic analysis and algorithmic issues Easily modified MATLAB library routines Enables 1D-3D solution of PDEs in general geometries Exercises at the end of each chapter Description for Sales People The text 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. This is the first text on DG-FEM, suitable both as a textbook and for self study. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEs, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEs. Attention is paid to both basic analysis and algorithmic issues. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters. Details ISBN0387720650 Author Tim Warburton Short Title NODAL DISCONTINUOUS GALERKIN M Series Texts in Applied Mathematics Language English ISBN-10 0387720650 ISBN-13 9780387720654 Media Book Format Hardcover DEWEY 515.353 Series Number 54 Year 2007 Imprint Springer-Verlag New York Inc. Subtitle Algorithms, Analysis, and Applications Place of Publication New York, NY Country of Publication United States Edition 2008th DOI 10.1604/9780387720654;10.1007/978-0-387-72067-8 UK Release Date 2007-12-18 AU Release Date 2007-12-18 NZ Release Date 2007-12-18 US Release Date 2007-12-18 Pages 502 Publisher Springer-Verlag New York Inc. Edition Description 2008 ed. Publication Date 2007-12-18 Alternative 9781441924636 Illustrations XIV, 502 p. Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:137849523;

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