This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic

Autorentext

Joel Chaskalovic is a Professor of Applied Mathematics at the University Pierre and Marie Curie in Paris and has written books and published papers in highly ranked journals, including the French Sciences Academy Journal, Journal of Computational Physics, journals in medicine etc.

This reflects the wide spectrum of his research work, which focuses on non-linear mathematical modeling and data mining techniques applied to fluid and solid mechanics, numerical analysis, complexity and randomness, biology and medicine, marketing, media and communication. Professor Chaskalovic has held numerous lectures on all of these topics at conferences worldwide.

Inhalt

Introduction to functional analytical methods of partial differential equations.- The finite element method.- Variational Formulations of elliptic boundary problems.- Finite Elements and differential Introduction to functional analytical methods of partial differential equations.- The finite element method.- Variational Formulations of elliptic boundary problems.- Finite Elements and differential boundary conditions.- Finite Elements in Deformable Solid Body Mechanics.- Finite Elements Applied to Strength of Materials.- Finite Elements Applied to Non Linear Problems.- Finite Elements in Deformable Solid Body Mechanics.- Finite Elements Applied to Strength of Materials.- Finite Elements Applied to Non Linear Problems.