The Mathematical Theory of Finite Element Methods

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities.

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations.

This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. 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.