Numerical Solution of Partial Differential Equations—III, SYNSPADE 1975

Numerical Solution of Partial Differential Equations—III: Synspade 1975 provides information pertinent to those difficult problems in partial differential equations exhibiting some type of singular behavior. This book covers a variety of topics, including the mathematical models and their relation to experiment as well as the behavior of solutions of the partial differential equations involved. Organized into 16 chapters, this book begins with an overview of elastodynamic results for stress intensity factors of a bifurcating crack. This text then discusses the effects of nonlinearities, such as bifurcation, which occur in problems of nonlinear mechanics. Other chapters consider the equations of changing type and those with rapidly oscillating coefficients. This book discusses as well the effective computational methods for numerical solutions. The final chapter deals with the principal results on G-convergence, such as the convergence of the Green's operators for Dirichlet's and other boundary problems. This book is a valuable resource for engineers and mathematicians.

Contributors

Preface

Elastostatic and Elastodynamic Stress Singularities

Fundamental Mathematical Problems in the Theory of Nonlinear Elasticity

Numerical Solution of Linear Partial Differential Equations of Elliptic-Hyperbolic Type

Homogenization and Its Application. Mathematical and Computational Problems

An Assessment of Current Finite Element Analysis of Nonlinear Problems in Solid Mechanics

Crude Numerical Approximation of Turbulent Flow

Heterogeneity Effects in Neutron Transport Computations

Behavior of the Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain

Numerical Solution of Nonlinear Partial Differential Equations of Mixed Type

Numerical Analysis of the Neutron Transport Equation

Instability Phenomena in Fluid Mechanics

Introduction to Some Aspects of Free Surface Problems

Regularity of Solutions of the Stokes Problem in a Polygonal Domain

Hyperbolic Equations in Regions with Characteristic Boundaries or with Corners

Numerical Bifurcation and Secondary Bifurcation: A Case History

Convergence in Energy for Elliptic Operators

Short Communications