The computational solution of partial differential systems has become so involved that it is important to automate decisions that have been left to the individual. This book covers such decisions: mesh generation with links to the software generating the domain geometry; and solution accuracy with mesh selection linked to solution generation.

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.

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