Hyperbolic Problems: Theory, Numerics, Applications: Eighth International Conference in Magdeburg, February/March 2000 Volume II

✍ Scribed by Bernard Haasdonk (auth.), Heinrich Freistühler, Gerald Warnecke (eds.)

• Publisher: Birkhäuser Basel
• Year: 2001
• Tongue: English
• Leaves: 470
• Series: ISNM International Series of Numerical Mathematics 141
• Edition: 1
• Category: Library

✦ Synopsis

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed.

This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems.

Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

✦ Table of Contents

Front Matter....Pages i-xii
Convergence of a Staggered Lax-Friedrichs Scheme on Unstructured 2D-grids....Pages 475-483
Viscous and Relaxation Approximations to Heteroclinic Traveling Waves of Conservation Laws with Source Terms....Pages 485-493
Adaptive Fe Methods for Conservation Equations....Pages 495-503
The Entropy Rate Admissibility Criterion for a Phase Transition Problem....Pages 505-513
Dust Formation in Turbulent Media....Pages 515-524
Existence of a Weak Solution for a Quasilinear Wave Equation with Boundary Condition....Pages 525-534
Asymptotic Behavior of Entropy Weak Solution for Hyperbolic System with Damping....Pages 535-542
On the Existence of Semidiscrete Shock Profiles....Pages 543-551
On the Convergence Rate of Operator Splitting for Weakly Coupled Systems of Hamilton-Jacobi Equations....Pages 553-562
Composite Schemes on Triangular Meshes....Pages 563-572
Asymptotic-Preserving (Ap) Schemes for Multiscale Kinetic Equations: a Unified Approach....Pages 573-582
A Kinetic Approach to Hyperbolic Systems And the Role of Higher Order Entropies....Pages 583-592
Stationary Waves for the Discrete Boltzmann Equations in the Half Space....Pages 593-602
Divergence Corrections in the Numerical Sim-ulation of Electromagnetic Wave Propagation....Pages 603-612
Numerical Investigation of Examples of Unstable Viscous Shock Waves....Pages 613-621
Proving Existence of Nonlinear Differential Equations Using Numerical Approximations....Pages 623-631
Asymptotic Behavior of Hyperbolic Boundary Value Problems with Relaxation Term....Pages 633-642
A Wave Propagation Algorithm for the Solution of PDEs on the Surface of a Sphere....Pages 643-652
On the L 1 Stability of Multi-shock Solutions to the Riemann Problem....Pages 653-661
Stable, Oscillatory Viscous Profiles of Weak Shocks in Systems of Stiff Balance Laws....Pages 663-672
Shallow Water Conservation Laws on a Sphere....Pages 673-682
Riemann Solutions for a Model of Combustion in Two-Phase Flow in Porous Media....Pages 683-692
Theory of Three-Phase Flow Applied to Water-Alternating-Gas Enhanced Oil Recovery....Pages 693-702
Preconditioned krylov subspace methods for Hyperbolic conservation laws....Pages 703-712
The Riemann Problem for Nonlinear Elasticity....Pages 713-722
ADER: Arbitrary-Order Non-Oscillatory Advection Schemes....Pages 723-732
Extended thermodynamics - the physics and Mathematics of the hyperbolic equations of Thermodynamics....Pages 733-754
Enforcing Gauss’ Law in Computational Elec-Tromagnetics Within a Finite-Volume Framework....Pages 755-764
Discrete BGK Models for Dynamic Phase Transitions in One-Dimension....Pages 765-774
An Adaptive Staggered Grid Scheme for Conservation Laws....Pages 775-784
Solutions to Scalar Conservation Laws Where the Flux is Discontinuous in Space and Time....Pages 785-790
Overcompressive Shocks and Compound Shocks in 2D and 3D Magnetohydrodynamic Flows....Pages 791-800
Aspects of a Numerical Procedure for Two-Phase Flow Models....Pages 801-810
On a Nonexistence of Global Smooth Solutions to Compressible Euler Equations....Pages 811-820
Central Schemes for Balance Laws....Pages 821-829
Estimates for Pseudo-differential and Hyperbolic Differential Equations via Fourier Integrals with Complex Phases....Pages 831-839
Existence of travelling fronts for Nonlinear transport equations....Pages 841-850
Nonlinear Wave Propagation in Close to Hyperbolic Systems....Pages 851-860
Shock-Wave C osmology....Pages 861-862
On a Second Order Residual Estimator for Nonlinear Conservation Laws....Pages 863-871
Error Estimates of Approximate Solutions for Nonlinear Scalar Conservation Laws....Pages 873-882
Solution of the Boltzmann Equation in Stiff Regime....Pages 883-890
Characteristics and Riemann Invariants of the Kinetic Integrodifferential Equations of Bubbly Flow....Pages 891-900
A LSQ-SPH Approach for Solving Compressible Viscous Flows....Pages 901-910
On Stability of Fast Shock Waves in Classical and Relativistic MHD....Pages 911-919
Remarks on Hyperbolic Relaxation Systems....Pages 921-929
Wave Interactions in Nonlinear Strings....Pages 931-939
Back Matter....Pages 941-946

✦ Subjects

Partial Differential Equations