Ebook: 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.

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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.
Content:
Front Matter....Pages i-li
NURBS and Grid Generation....Pages 1-21
Coping with Degeneracies in Delaunay Triangulation....Pages 23-30
Geometric Approaches to Mesh Generation....Pages 31-51
Refining Quadrilateral and Brick Element Meshes....Pages 53-65
Automatic Meshing of Curved Three—Dimensional Domains: Curving Finite Elements and Curvature-Based Mesh Control....Pages 67-96
Optimization of Tetrahedral Meshes....Pages 97-127
A Class of Error Estimators Based on Interpolating the Finite Element Solutions for Reaction-Diffusion Equations....Pages 129-151
Accuracy-Based Time Step Criteria for Solving Parabolic Equations....Pages 153-163
Adaptive Domain Decomposition Methods for Advection-Diffusion Problems....Pages 165-186
A Characteristic-Galerkin Method for the Navier-Stokes Equations in Thin Domains with Free Boundaries....Pages 187-199
Parallel Partitioning Strategies for the Adaptive Solution of Conservation Laws....Pages 201-213
A Knowledge-Based Approach to the Adaptive Finite Element Analysis....Pages 215-242
An Asymptotically Exact, Pointwise, A Posteriori Error Estimator for the Finite Element Method with Super Convergence Properties....Pages 243-265
A Mesh-Adaptive Collocation Technique for the Simulation of Advection-Dominated Single- and Multiphase Transport Phenomena in Porous Media....Pages 267-276
Three-Step H-P Adaptive Strategy for the Incompressible Navier-Stokes Equations....Pages 277-305
Applications of Automatic Mesh Generation and Adaptive Methods in Computational Medicine....Pages 307-346
Solution of Elastic-Plastic Stress Analysis Problems by the P-version of the Finite Element Method....Pages 347-366
Adaptive Finite Volume Methods for Time-Dependent P.D.E.S.....Pages 367-393
Superconvergence of the Derivative Patch Recovery Technique and A Posteriori Error Estimation....Pages 395-416
....Pages 417-430