Course code TUD01
Course title Introduction into Finite Elements and Algorithms
Institution Delft University of Technology
Course address Numerical Analysis Group - Delft Institute of Applied Mathematics (DIAM) - TU Delft
City Delft
Minimum year of study 3rd year
Minimum level of English Fluent
Minimum level of French None
Key words

Finite Element Method, Poisson Equation, Heat Equation

Language English
Professor responsible Dr. Domenico Lahaye
Telephone +31.015.27.87.257
Fax +31.015.27.87.209
Email d.j.p.lahaye@tudelft.nl
Participating professors

Dr. D. Lahaye

Number of places Minimum: 40, Maximum: 45, Reserved for local students:
Objectives

This course provides understanding in the basic principles of the finite element method (FEM) for solving canonical elliptic and parabolic partial differential equations modeling diffusion and transport phenomena. Unlike courses elaborating the mathematical foundations of the FEM on one hand, and those focussing on a particular software package for solving advanced engineering applications on the other end of the spectrum, this course discusses the algorithmic aspects of the FEM. Starting from either a boundary or initial value problem, the variational formulation is derived to be able to subsequentially discretize the problem in space and time. The element-by-element construction of the discrete problem and algorithms to solve it are presented. At the end of this course students will have gained the theoretical knowledge and constructed a software framework enabling them to build their own finite element solver package.


 


 
Programme to be followed

Monday afternoon: introduction to programming in Matlab.

Tuesday through Thursday: lectures in the morning and lab sessions in the afternoon.

Friday morning: lab session.  

Friday afternoon: presentations by industrial partners. 


 
Prerequisites

Following this course requires having succesfully completed a first year course in linear algebra (thus being familiar with vector spaces and linear systems of equations, see e.g. David Lay, Linear Algebra and Its Applications); in calculus (thus being familiar with the differention and integration of functions of several variables and analytical methods for solving ordinary differential equations, see e.g. James Stewart, Calculus); and in numerical analysis (thus being familiar with numecal techniques for differentiation and integration of a function in one variable, see e.g. Richard Burden and Douglas Faires, Numerical Analysis).

For this course a basic knowledge of English is indispensable.





Course exam

By active participation in the lectures in the morning and by completion of the lab sessions in the afternoon.

More information: more information on the course is available at http://ta.twi.tudelft.nl/nw/users/domenico/intro_fem/intro_fem.html
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