Front Cover; Numerical Methods for Partial Differential Equations; Copyright Page; Table of Contents; CONTRIBUTORS; PREFACE; Chapter 1. Finite Element Formulation, Modeling, and Solution of Nonlinear Dynamic Problems; ABSTRACT; 1. INTRODUCTION; 2. FINITE ELEMENT FORMULATION AND SOLUTION; 3. FINITE ELEMENT MODELING FOR DYNAMIC ANALYSIS; 4. SOME STABILITY AND ACCURACY CONSIDERATIONS; 5. DEMONSTRATIVE SAMPLE SOLUTIONS; 6. CONCLUSIONS; REFERENCES; ACKNOWLEDGEMENT; Chapter 2. Discrete Methods for Parabolic Equations with Time-Dependent Coefficients; I. INTRODUCTION; II. SPACIAL DISCRETIZATION

III. TIME DISCRETIZATIONIV. HIGH ORDER EFFICIENT METHODS; REFERENCES; Chapter 3. Multigrid Solutions to Elliptic Flow Problems; ABSTRACT; 1. INTRODUCTION; 2. MULTI-GRID ALGORITHMS; 3. ELLIPTIC DIFFERENCE EQUATIONS AND SYSTEMS; 4. LOCAL MODE ANALYSIS OF MULTI-LEVEL PROCESSES; 5. CAUCHY-RIEMANN EQUATIONS; 6. STEADY-STATE STOKES EQUATIONS; 7. STEADY-STATE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS; REFERENCES; ACKNOWLEDGEMENT; Chapter 4. Computational Fluid Dynamics; 1. INTRODUCTION; 2. DIFFERENTIAL EQUATIONS AND BOUNDARY CONDITIONS. IMPORTANT PARAMETERS AND FLOW PHENOMENA

3. NUMERICAL DISSIPATION AND DISPERSION4. TIME-DEPENDENT GAS DYNAMICS AND SHOCK WAVES; 5. STEADY FLOWS; 6. NAVIER-STOKES EQUATIONS; 7. STREAM-FUNCTION AND VORTICITY METHODS; 8. INVISCID FLOWS WITH VORTEX SHEETS -- FORMATION OF HILL'S VORTEX; REFERENCES; Chapter 5. The Numerical Solution of a Degenerate Variational Inequality; 1. ELASTIC-PLASTIC TORSION OF AN AXISYMMETRIC SHAFT; 2. THE ONE-DIMENSIONAL CLASSICAL PROBLEM; 3. ALTERNATIVE FORMULATIONS OF THE ONE-DIMENSIONAL ELASTIC-PLASTIC PROBLEM; 4. THE TWO-DIMENSIONAL COMPLEMENTARITY PROBLEM AND VARIATIONAL INEQUALITY; 5. NUMERICAL APPROXIMATION

6. OTHER APPLICATIONS OF VARIATIONAL INEQUALITIESREFERENCES; Chapter 6. Simplified Solution Algorithms for Fluid Flow Problems; ABSTRACT; I. INTRODUCTION; II. SOLA-A SOLUTION ALGORITHM FOR INCOMPRESSIBLE FLUID FLOW; III. MODIFICATIONS OF THE BASIC ALGORITHM; IV. Acknowledgments; REFERENCES; Chapter 7. Numerical Methods for Hyperbolic Partial Differential Equations; 1. INTRODUCTION; 2. THE CAUCHY PROBLEM FOR HYPERBOLIC SYSTEMS IN ONE SPACE DIMENSION; 3. THE CAUCHY PROBLEM FOR HYPERBOLIC SYSTEMS IN MORE THAN ONE SPACE DIMENSION; 4. INITIAL-BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC SYSTEMS

5. DIFFERENCE APPROXIMATION FOR THE CAUCHY PROBLEM6. STABILITY CONDITIONS; 7. PROPAGATION OF DISCONTINUITIES; 8. DIFFERENCE APPROXIMATIONS FOR INITIAL BOUNDARY VALUE PROBLEMS; REFERENCES; Chapter 8. Constructing Stable Difference Methods for Hyperbolic Equations; I. INTRODUCTION; II. THE PROBLEM, NOTATION AND BACKGROUND MATERIAL; III. STABILITY RESULTS; IV. METHODS FOR THE DERIVATION OF UNCENTERED CAUCHY STABLE DISSIPATIVE APPROXIMATIONS; REFERENCES; Chapter 9. Spectral Methods for Problems in Complex Geometrics; 1. INTRODUCTION; 2. BOUNDARY CONDITIONS