Discontinuous Galerkin Methods
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1 Bernardo Cockburn George E. Karniadakis Chi-Wang Shu (Eds.) Discontinuous Galerkin Methods Theory,Computation and Applications With 138 Figures m s P rin B er
2 Table of Contents Part I Overview The Development of Discontinuous Galerkin Methods Bernardo Cockburn, George E. Karniadakis, and Chi-Wang Shu 3 Part II Invited Papers Steps Toward a Robust High-Order Simulation Tool for Aerospace Applications Harold L. Atkins 53 Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension Timothy J. Barth 63 A High Order Discontinuous Galerkin Method for Compressible Turbulent Flows Francesco Bassi and Stefano Rebay 77 Discontinuous Galerkin Methods for Elliptic Problems Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, and Donatella Marini 89 Analysis of Finite Element Methods for Linear Hyperbolic Problems Richard S. Falk 103 Software for the Parallel Adaptive Solution of Conservation Laws by Discontinuous Galerkin Methods Joseph E. Flaherty, Raymond M. Loy, Mark S. Shephard, and Jim D. Teresco 113 Simulation of Gravity Flow of Granulär Materials in Silos Pierre A. Gremaud and John V. Matthews 125
3 VIII Table of Contents A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Efnciency Thomas J.R. Hughes, Gerald Engel, Luca Mazzei, and Mats G. Larson 135 The Utility of Modeling and Simulation in Determining Transport Performance Properties of Semiconductors Bernardo Cockburn, Joseph W. Jerome, and Chi-Wang Shu. 147 A Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations Ohannes Karakashian and Theodoros Katsaounis 157 Füll Convergence for Hyperbolic Finite Elements Qun hin 167 A Conservative DGM for Convection-Diffusion and Navier-Stokes Problems J. Tinsley Oden and Carlos Erik Baumann 179 GMRES Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations Francesco Bassi and Stefano Rebay 197 Explicit Finite Element Methods for Linear Hyperbolic Systems Richard S. Falk and Gerard R. Richter 209 hp-dgfem for Partial Differential Equations with Nonnegative Characteristic Form Endre Süli, Christoph Schwab, and Paul Houston 221 A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations Beatrice Riviere and Mary F. Wheeler 231 Part III Contributed Papers Parallel Iterative Discontinuous Galerkin Finite-Element Methods Dan Aharoni and Amnon Barak 247 A Discontinuous Projection Algorithm for Hamilton Jacobi Equations Steeve Augoula and Remi Abgrall 255
4 Table of Contents IX Successes and Failures of Discontinuous Galerkin Methods in Viscoelastic Fluid Analysis Arjen C.B. Bogaerds, Wilco M.H. Verbeeten, and Frank P. T. Baaijens 263 High Order Current Basis Functions for Electromagnetic Scattering of Curved Surfaces WeiCai 271 An Adaptive Discontinuous Galerkin Model for Coupled Viscoplastic Crack Growth and Chemical Transport Fernando L. Carranza and R.B. Haber 277 An Optimal Estimate for the Local Discontinuous Galerkin Method Paul Castillo 285 Post-Processing of Galerkin Methods for Hyperbolic Problems Bernardo Cockburn, Mitchell Luskin, Chi-Wang Shu, and Endre Süli Introduction to Discontinuous Wavelets Nicholas Coult 301 The Local Discontinuous Galerkin Method for Contaminant Transport Problems Clint Dawson, Vadym Aizinger, and Bernardo Cockburn 309 Discontinuous Galerkin Method for the Numerical Solution of Euler Equations in Axisymmetric Geometry Bruno Despres 315 Ten Years Using Discontinuous Galerkin Methods for Polymer Processing Problems Andre Fortin, Alain Beliveau, Marie-Claude Heuzey, and Alain Lioret 321 Using Krylov-Subspace Iterations in Discontinuous Galerkin Methods for Nonlinear Reaction-Diffusion Systems Donald J. Estep and Roland W. Freund 327 An Abridged History of Cell Discretization John Greenstadt 337 The Effect of the Least Square Procedure for Discontinuous Galerkin Methods for Hamilton-Jacobi Equations Changqing Hu, Olga Lepsky, and Chi- Wang Shu 343
5 X Table of Contents A Posteriori Error Estimate in the Case of Insufficient Regularity of the Discrete Space Guido Kanschat and Franz-Theo Suttmeier 349 Discontinuous Spectral Element Approximation of Maxwell's Equations David A. Kopriva, Stephen L. Woodruff, and M. Y. Hussaini 355 A Posteriori Error Estimation for Adaptive Discontinuous Galerkin Approximations of Hyperbolic Systems Mats G. Larson and Timothy J. Barth 363 A Numerical Example on the Performance of High Order Discontinuous Galerkin Method for 2D Incompressible Flows Jian-Guo Liu and Chi- Wang Shu 369 A Discontinuous Galerkin Method in Moving Domains Igor Lomtev, Robert M. Kirby, and George E. Karniadakis 375 Discontinuous Galerkin for Hyperbolic Systems with Stiff Relaxation Robert B. Lowrie and Jim E. Morel 385 Finite Element Output Bounds for Parabolic Equations: Application to Heat Conduction Problems Luc Machiels 391 3D Unstructured Mesh ALE Hydrodynamics with the Upwind Discontinuous Galerkin Method Manoj K. Prasad, Jose L. Milovich, Aleksei I. Shestakov, David S. Kershaw and Michael J. Shaw 397 Some Remarks on the Accuracy of a Discontinuous Galerkin Method Patrick Rasetarinera, Mohammed Y. Hussaini, and Fang Q. Hu 407 Coupling Continuous and Discontinuous Techniques: An Adaptive Approach Mirko Sardella 413 A Discontinuous Galerkin Method for the Shallow Water Equations with Source Terms Dirk Schwanenberg and Jürgen Köngeter 419 Dispersion Analysis of the Continuous and Discontinuous Galerkin Formulations Spencer Sherwin 425
6 Table of Contents XI The Cell Discretization Algorithm; An Overview Howard Swann 433 Accuracy, Resolution, and Computational Complexity of a Discontinuous Galerkin Finite Element Method Härmen van der Ven and J. J. W. van der Vegt An ELL AM S eherne for Porous Medium Plows Hong Wang Application of the Discontinuous Galerkin Method to MaxwelFs Equations Using Unstructured Polymorphie hp-finite Elements Tim Warburton A Space-Time Discontinuous Galerkin Method for Elastodynamic Analysis Lin Yin, Amit Acharya, Nahil Sobh, Robert B. Haber, and Daniel A. Tortorelli 459 Nonconforming, Enhanced Strain, and Mixed Finite Element Methods - A Unified Approach Zhimin Zhang 465
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