Description
Book SynopsisSince the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Table of ContentsMotivation for the Study of Singular Perturbation Problems; Simple Examples of Singular Perturbation Problems; Numerical Methods for Singular Perturbation Problems; Fitted Operator Methods; Simple Fitted Mesh Methods in One Dimension; Fitted Mesh Methods for Reaction-Diffusion Problems; Properties of Upwind Operators on Piecewise Uniform Meshes; Fitted Mesh Methods for Convection-Diffusion Problems; Fitted Element Methods for Convection-Diffusion Problems; Schwarz Iterative Methods in One Dimension; Convection-Diffusion Problems in Two Dimensions; Bounds on Derivatives of Solutions of Convection-Diffusion Problems; Convergence of Fitted Mesh Methods in Two Dimensions; Limitations of Fitted Operators for Parabolic Boundary Layers; Initial and Parabolic Boundary Layers.
