Course Code : | 2001WETEEM |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Hans Vande Sande |

At the start of this course the student should have acquired the following competences:

a passive knowledge of

general notion of the basic concepts of

specific prerequisites for this course

a passive knowledge of

- English

- general knowledge of the use of a PC and the Internet

general notion of the basic concepts of

matlab

specific prerequisites for this course

Knowledge of Dutch is not strictly required, yet authorization for teaching in English will have to be asked by the lecturer.

- By the end of the theoretic part, students will be able to formulate a finite element problem for some common partial differential equations and systems of coupled partial differential equations;
- they can transform the mathematical formulation into an algebraic system of equations;
- they know the basic similarities and differences between finite element methods, finite difference methods, finite volume methods and boundary element methods;
- they can explain and formulate solutions for some method-specific issues, such as spurious oscillations when dealing with convection dominant problems;
- they will be sufficienty skilled to study mathematical as well as technical articles on the subject of finite elements;
- they can argue on the risks associated with using commercial simulation tools when not having any idea about the mathematical foundations used in such tools.
- By the end of the practical part, students will have demonstrated some theoretical issues using their own implementations;
- they will have implemented their own finite element solver for static as well as transient two-dimensional convection-diffusion problems.
- From teh company visit, the students will understand the importance of various numerical techniques for industry.

The course starts with a demo session, during which the use of the finite element method will be illustrated and in which a link is made with various aspects of the course. Next, the basic principles of the finite element method will be applied to a few simple but typical one-dimensional differential equations. Once this has been clearly understood, the finite element method will be generalized for solving some typical more-dimensional differential equations, and a more general mathematical framework will be given. Later on, some aspects such as the finite element solution of non-linear and/or transient problems will be discussed. The course ends with a visit to a private company, during which the importance of finite element methods for industry will be outlined.

Class contact teachingLectures Seminars/Tutorials Laboratory sessions

Personal workAssignments Individually

Excursions

Personal work

Excursions

ExaminationOral with written preparation Open book Open-question

Continuous assessmentAssignments Participation in classroom activities

Continuous assessment

During the lecture series, the lecturer will set relevant information (papers, presentations, etc.) to the disposal of the students.

Zienkiewicz O.C. & Taylor R.L., *The finite element method. Vol. I. Basic formulations and **linear problems*. McGraw-Hill, London, 1989.

Brenner S.C. & Ridgway Scott L., *The mathematical theory of finite element methods*. Springer, New York, 2002.

Silvester P.P. & Ferrari R. L., *Finite elements for electrical engineers*. Cambridge University Press, Cambridge, 1996.

The lecturer can always be contacted by e-mail: hans.vandesande@uantwerpen.be