Discontinuous Galerkin Methods: Theory, Computation and Applications,9783540667872

Discontinuous Galerkin Methods: Theory, Computation and Applications

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ISBN13: 9783540667872
ISBN10: 3540667873
Format: Hardcover
Pub. Date: 2000-03-01
Publisher(s): Springer Verlag
List Price: $105.92

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Summary

This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simulation, turbomachinery, turbulent flows, materials processing, Magneto-hydro-dynamics, plasma simulations and image processing. While there has been a lot of interest in DGM from mathematicians, physicists and engineers, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. The current volume organizes this knowledge and it covers both theoretical as well as practical issues of the Discontinuous Galerkin method.

Table of Contents

Part I Overview
The Development of Discontinuous Galerkin Methods
3(50)
Bernardo Cockburn
George E. Karniadakis
Chi-Wang Shu
Part II Invited Papers
Steps Toward a Robust High-Order Simulation Tool for Aerospace Applications
53(10)
Harold L. Atkins
Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension
63(14)
Timothy J. Barth
A High Order Discontinuous Galerkin Method for Compressible Turbulent Flows
77(12)
Francesco Bassi
Stefano Rebay
Discontinuous Galerkin Methods for Elliptic Problems
89(14)
Douglas N. Arnold
Franco Brezzi
Bernardo Cockburn
Donatella Marini
Analysis of Finite Element Methods for Linear Hyperbolic Problems
103(10)
Richard S. Falk
Software for the Parallel Adaptive Solution of Conservation Laws by Discountinuous Galerkin Methods
113(12)
Joseph E. Flaherty
Raymond M. Loy
Mark S. Shephard
Jim D. Teresco
Simulation of Gravity Flow of Granular Materials in Silos
125(10)
Pierre A. Gremaud
John V. Matthews
A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Efficiency
135(12)
Thomas J.R. Hughes
Gerald Engel
Luca Mazzei
Mats G. Larson
The Utility of Modeling and Simulation in Determining Transport Performance Properties of Semiconductors
147(10)
Bernado Cockburn
Joseph W. Jerome
Chi-Wang Shu
A Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations
157(10)
Ohannes Karakashian
Theodoros Katsaounis
Full Convergence for Hyperbolic Finite Elements
167(12)
Qun Lin
A Conservative DGM for Convection-Diffusion and Navier-Stokes Problems
179(18)
J. Tinsley Oden
Carlos Erik Baumann
GMRES Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations
197(12)
Francesco Bassi
Stefano Rebay
Explicit Finite Element Methods for Linear Hyperbolic Systems
209(12)
Richard S. Falk
Gerard R. Richter
hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form
221(10)
Endre Suli
Christoph Schwab
Paul Houston
A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations
231(16)
Beatrice Riviere
Mary F. Wheeler
Part III Contributed Papers
Parallel Iterative Discontinuous Galerkin Finite-Element Methods
247(8)
Dan Aharoni
Amnon Barak
A Discontinuous Projection Algorithm for Hamilton Jacobi Equations
255(8)
Steeve Augoula
Remi Abgrall
Successes and Failures of Discontinuous Galerkin Methods in Viscoelastic Fluid Analysis
263(8)
Arjen C. B. Bogaerds
Wilco M.H. Verbeeten
Frank P.T. Baaijens
High Order Current Basis Functions for Electromagnetic Scattering of Curved Surfaces
271(6)
Wei Cai
An Adaptive Discontinuous Galerkin Model for Coupled Viscoplastic Crack Growth and Chemical Transport
277(8)
Fernando L. Carranza
R. B. Haber
An Optimal Estimate for the Local Discontinuous Galerkin Method
285(6)
Paul Castillo
Post-Processing of Galerkin Methods for Hyperbolic Problems
291(10)
Bernardo Cockburn
Mitchell Luskin
Chi-Wang Shu
Endre Suli
Introduction to Discontinuous Wavelets
301(8)
Nicholas Coult
The Local Discontinuous Galerkin Method for Contaminant Transport Problems
309(6)
Clint Dawson
Vadym Aizinger
Bernardo Cockburn
Discontinuous Galerkin Method for the Numerical Solution of Euler Equations in Axisymmetric Geometry
315(6)
Bruno Despres
Ten Years Using Discontinuous Galerkin Methods for Polymer Processing Problems
321(6)
Andre Fortin
Alain Beliveau
Marie-Claude Heuzey
Alain Lioret
Using Krylov-Subspace Iterations in Discontinuous Galerkin Methods for Nonlinear Reaction-Diffusion Systems
327(10)
Donald J. Estep
Roland W. Freund
An Abridged History of Cell Discretization
337(6)
John Greenstadt
The Effect of the Least Square Procedure for Discontinuous Galerkin Methods for Hamilton-Jacobi Equations
343(6)
Changging Hu
Olga Lepsky
Chi-Wang Shu
A Posteriori Error Estimate in the Case of Insufficient Regularity of the Discrete Space
349(6)
Guido Kanschat
Franz-Theo Suttmeier
Discontinuous Spectral Element Approximation of Maxwell's Equations
355(8)
David A. Kopriva
Stephen L. Woodruff
M. Y. Hussaini
A Posteriori Error Estimation for Adaptive Discontinuous Galerkin Approximations of Hyperbolic Systems
363(6)
Mats G. Larson
Timothy J. Barth
A Numerical Example on the Performance of High Order Discontinuous Galerkin Method for 2D Incompressible Flows
369(6)
Jian-Guo Liu
Chi-Wang Shu
A Discontinuous Galerkin Method in Moving Domains
375(10)
Igor Lomtev
Robert M. Kirby
George E. Karniadakis
Discontinuous Galerkin for Hyperbolic Systems with Stiff Relaxation
385(6)
Robert B. Lowrie
Jim E. Morel
Finite Element Output Bounds for Parabolic Equations: Application to Heat Conduction Problems
391(6)
Luc Machiels
3D Unstructured Mesh ALE Hydrodynamics with the Upwind Discontinuous Galerkin Method
397(10)
Manoj K. Prasad
Jose L. Milovich
Aleksei I. Shestakov
David S. Kershaw
Michael J. Shaw
Some Remarks on the Accuracy of a Discontinuous Galerkin Method
407(6)
Patrick Rasetarinera
Mohammed Y. Hussaini
Fang Q. Hu
Coupling Continuous and Discontinuous Techniques: An Adaptive Approach
413(6)
Mirko Sardella
A Discontinuous Galerkin Method for the Shallow Water Equations with Source Terms
419(6)
Dirk Schwanenberg
Jurgen Kongeter
Dispersion Analysis of the Continuous and Discontinuous Galerkin Formulations
425(8)
Spencer Sherwin
The Cell Discretization Algorithm; An Overview
433(6)
Howard Swann
Accuracy, Resolution, and Computational Complexity of a Discontinuous Galerkin Finite Element Method
439(6)
Harmen van der Ven
J.J.W. van der Vegt
An ELLAM Scheme for Porous Medium Flows
445(6)
Hong Wang
Application of the Discontinuous Galerkin Method to Maxwell's Equations Using Unstructured Polymorphic hp-Finite Elements
451(8)
Tim Warburton
A Space-Time Discontinuous Galerkin Method for Elastodynamic Analysis
459(6)
Lin Yin
Amit Acharya
Nahil Sobh
Robert B. Haber
Daniel A. Tortorelli
Nonconforming, Enhanced Strain, and Mixed Finite Element Methods A Unified Approach
465
Zhimin Zhang

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