Finite element methods: theory, applications and implementation

Abstract

The aim of these lecture notes is to acquaint the reader with the numerical solution of partial differential equations with the use of modern techniques represented by the finite element and discontinuous Galerkin methods. Our aim is not to give a complete overview of the application of these methods to the solution of arbitrary differential equations.

These lecture notes should serve as a basic study material on this subject, helping the readers to orient themselves within the finite element methods and to understand the essentials of more sophisticated approaches and techniques.

Keywords

• finite element method
• elliptic problems
• convection-diffusion equations
• incompressible fluid flow
• evolution problems
• discontinuous Galerkin method
• error estimates
• implementation