The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities.

This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.

Patrick Ciarlet is a professor at the Applied Mathematics Unit of ENSTA Paris, France. His research focuses on the design of numerical methods for solving problems in physics, modeled by systems of partial differential equations.

Eric Lunéville is a professor at the Applied Mathematics Unit of ENSTA Paris, France. His research focuses on the design of numerical methods for solving problems in mechanics and physics, modeled by systems of partial differential equations.