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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.
Preface.
Introduction.
Fundamentals.
Variational Formulation of Boundary Problems.
Introduction to Finite Element.
Non-conforming Methods.
Nodal Methods.
Positive Symmetric First-Order Systems Within the Meaning of Friedrichs.
Approximation of the Transport Equation in Plane Two-Dimensional Geometry by Continuous and Discontinuous Finite Element Methods.
Exercises with Solutions.
Revision Issues.
Index