This book discusses major topics and problems in finite element methods. It is targeted to graduate students and researchers in applied mathematics, physics, and engineering, wishing to learn and familiarize themselves with finite element theory. The book describes the nodal method for squares or rectangles and triangles, as well as an increase of the error between exact solution and approximate solution. It discusses an approximation of positive symmetric first-order systems in the Friedrichs sense by finite element methods. In addition, the book also explains the continuous and discontinuous approximation methods, adapted to the structure of the transport equation, leading to linear systems of quasi-explicit resolution, and therefore commonly used in practice.

Discusses an approximation of positive symmetric first-order systems in the Friedrichs sense by finite element methods Describes the nodal method for rectangles and triangles and the error between exact solution and approximate solution Targets applied mathematicians, engineers, scientists, and graduate students of mathematics and engineering

Autorentext

Aymen Ammar is Professor at the Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia. He is a co-author of the book, Spectral Theory of Multivalued Linear Operators, with Aref Jeribi. He has published more than 111 paper in several international journals. His areas of interest include spectral theory, matrix operators, transport theory, and linear relations. Aref Jeribi is Professor in the Department of Mathematics, University of Sfax, Tunisia. He completed his Habilitation of Mathematics and Applications at the University of Sfax, Tunisia, in 2002, and defended his PhD thesis at the University of Corsica Pasquale Paoli, France, in 1998. His research interests include spectral theory, matrix operators, transport theory, Gribov operator, Bargmann space, fixed point theory, Riesz basis and linear relations. He is an author of 13 books, including Problems in Finite Element Methods Aubin Nitsche’s Duality Process, Nodal Methods and Friedrichs Systems, (Springer, 2025), Perturbation Theory for Linear Operators: Denseness and Bases with Applications (Springer, 2021) and Spectral Theory and Applications of Linear Operators and Block Operator Matrices (Springer, 2015) and more than 234 research articles published in reputed journals and conference proceedings.

Inhalt

Chapter 1 Introduction.- Chapter 2 Fundamentals.- Chapter 3 Variational Formulation of Boundary Problems.- Chapter 4 Introduction to Finite Elements.- Chapter 5 Non-conforming Methods.- Chapter 6 Nodal Methods.