Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.

Week 1.- NURBS and grid generation.- Coping with degeneracies in Delaunay triangulation.- Geometric approaches to mesh generation.- Refining quadrilateral and brick element meshes.- Automatic meshing of curved three—dimensional domains: Curving finite elements and curvature-based mesh control.- Week 2.- Optimization of tetrahedral meshes.- A class of error estimators based on interpolating the finite element solutions for reaction-diffusion equations.- Accuracy-based time step criteria for solving parabolic equations.- Week 3.- Adaptive domain decomposition methods for advection-diffusion problems.- LP-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems.- A characteristic-Galerkin method for the Navier-Stokes equations in thin domains with free boundaries.- Parallel partitioning strategies for the adaptive solution of conservation laws.- Adaptive multi-grid method for a periodic heterogeneous medium in 1 ? D.- A knowledge-based approach to the adaptive finite element analysis.- An asymptotically exact, pointwise, a posteriori error estimator for the finite element method with super convergence properties.- A mesh-adaptive collocation technique for the simulation of advection-dominated single- and multiphase transport phenomena in porous media.- Three-step H-P adaptive strategy for the incompressible Navier-Stokes equations.- Applications of automatic mesh generation and adaptive methods in computational medicine.- Solution of elastic-plastic stress analysis problems by the p-version of the finite element method.- Adaptive finite volume methods for time-dependent P.D.E.S.- Superconvergence of the derivative patch recovery technique and a posteriori error estimation.