This book shows the latest frontiers of the research by the most active researchers in the field of numerical mathematics. The papers in the book were presented in a symposium at Yamaguchi, Japan. The subject of the symposium was mathematical modeling and numerical simulation in continuum mechanics. The topics of the lectures ranged from solids to fluids and included both mathematical and computational analysis of phenomena and algorithms. The readers can study the latest results on shells, plates, flows in various situations, fracture of solids, new ways of exact error estimates and many other topics.

Nonlinear Shell Models of Koiter's Type.- A Survey of Stabilized Plate Elements.- Prediction of the Fatigue Crack Growth Life in Microelectronics Solder Joints.- Multi-phase Flow with Reaction.- Universal and Simultaneous Solution of Solid, Liquid and Gas in Cartesian-Grid-Based CIP Method.- Subgrid Phenomena and Numerical Schemes.- Two Scale FEM for Homogenization Problems.- Numerical Analysis of Electromagnetic Problems.- A-priori Domain Decomposition of PDE Systems and Applications.- A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis.- Essential Spectrum and Mixed Type Finite Element Method.- Can We Trust the Computational Analysis of Engineering Problems?.- Numerical Computations for Ill-conditioned Problems by Multiple-Precision Systems.- Numerical Verification Methods for Solutions of Free Boundary Problems.- Pattern Formation of Heat Convection Problems.- Mathematical Modeling and Numerical Simulation of Earth's Mantle Convection.- Theoretical and Numerical Analysis on 3-Dimensional Brittle Fracture.- Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems.- A New Fast Multipole Boundary Integral Equation Method in Elastostatic Crack Problems in 3D.- Computational Crack Path Prediction and the Singularities in Elastic-Plastic Stress Fields.