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A guide to numerical methods for solving large sparse linear systems of equations, in particular those arising from the discretization of partial differential equations. This text covers both direct and iterative methods, including Gaussian elimination and alternating directions algorithms.

Albert Cohen's main objectives are to survey the theoretical results that are involved in the numerical analysis of wavelet methods, and more generally of multiscale decomposition methods, for numerical simulation problems, and to provide relevant examples and applications.

Shows how asymptotic methods, with the thickness as the small parameter, indeed provide a means of justifying two-dimensional plate theories. This book demonstrates that asymptotic methods can be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures.

Presents the main approaches developed for a posteriori error estimation in various problems. This book contains a number of mathematical results and lists a posteriori error estimation methods. It includes computable bounds of approximation, errors checking algorithms, iteration processes, finite element methods, and more.

In accordance with the developments in computation, theoretical studies on numerical schemes are needed. This book studies various schemes from operator theoretical points of view. It includes chapters such as: Boundary Value Problems and FEM; Semigroup Theory and FEM; Evolution Equations and FEM; Other Methods in Time Discretization; and more.

Contains the written versions of lectures delivered since 1997 in the weekly seminar on Applied Mathematics at the College de France in Paris, directed by Jacques-Louis Lions. This book includes texts that deal with various aspects of the theory of nonlinear partial differential equations.