This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It introduces the main principles of discretization and details the ideas and analysis of advanced numerical methods in the area.

This book deals with discretization techniques for elliptic, parabolic and hyperbolic partial differential equations. It provides an introduction to the main principles of discretizations and presents to the reader the ideas and analysis of advanced numerical methods in this area. The book also covers recent research developments - these topics of current interest are rarely considered in other textbooks. It is the authors' aim to give mathematically-inclined students, scientists and engineers a textbook that contains all the basic discretization techniques for the three fundamental types of partial differential equations and in which the reader can find analytical tools, properties of discretizations, and some advice on algorithmic aspects. While finite element methods are the main focus of the book, finite difference methods and finite volume techniques are also presented. Furthermore, the book provides the basic tools needed to solve the discrete problems generated.

Includes supplementary material: sn.pub/extras

Contenu
Partial Differential Equations: Basics and Explicit Representation of Solutions.- Finite Difference Methods.- Weak Solutions, Elliptic Problems and Sobolev Spaces.- The Finite Element Method.- Finite Element Methods for Unsteady Problems.- Singular Perturbations.- Numerical Methods for Variational Inequalities and Optimal Control.- Numerical Methods for Discretized Problems.