Problems in Finite Element Methods : Aubin Nitsche?s Duality Process, Nodal Methods and Friedrichs Systems

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.

Aref Jeribi is Professor in the Department of Mathematics and Statistics, College of science, Imam Mohammad Ibn Saud Islamic, Riyadh, Saudi Arabia, and in the Department of Mathematics, University of Sfax, Sfax, Tunisia. He completed his Habilitation of Mathematics and Applications at the University of Sfax, Tunisia, in 2002, and defended his Ph.D. 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.