Course syllabus - Finite Element Method

Objectives

The course aims at giving knowledge about the theory and the applications of finite element method.

Learning outcomes

At the end of a passed course, the student is expected to be able to

- utilize partial derivatives for determining whether a function solves a partial differential equation (PDE), and also to be able to handle concepts of norms and scalar product

- by physical laws obtain PDE with given boundary conditions

- determine whether a problem is well-posed or not, and also to be able to classify different types of PDE

- write PDE in variational form

- discretise the problem domain in a net by finite element

- by the finite element method implementing and solving second order elliptic boundary-value problems in one spatial dimension with Dirichlet-, Neumann- and Robin boundary-value conditions respectively

- by the finite element method formulate and with a  computer solve second order elliptic PDE in two spatial dimensions with Dirichlet-, Neumann- and Robin boundary values respectively

- utilize the software available for solving more complicated problems, like coupled systems of equations

Course content

- Definition of elliptic, hyperbolic and parabolic PDE. Definition of well-ordered problems. Dirichlet-, Neumann- and Robin boundary

- Value conditions. Discrete function spaces in one and in two dimensions. Norm and scalar product in discrete function spaces

- Variational formulations of elliptic boundary-value problems

- Finite element method in one and in two dimensions. Maximum principle, the discrete and the continuous. Error estimates for approximations by finite element method (FEM) of elliptic problems. Mesh division and adaptive mesh refinement. Implementation of FEM in MATLAB. Utilization of FEM-software

Tuition

Teaching is given in the form of lectures, classes and laboratory work.

Specific requirements

At least 60 credits in the technical, natural sciences, business administration or economics areas including Calculus of Several Variables 7,5 credits or the equivalent, Numerical Methods with MATLAB 7,5 credits or a course equivalent to Programming 7,5 hp and also either Applied Matrix Analysis 7,5 credits or Linear Algebra 7,5 credits or the equivalent.

Examination

Assigned problems (INL1), 1 credits, mark Pass (G)
Computer laboratory work (LAB1), 1,5 credits, marks Fail (U), 3, 4 or 5
Computer laboratory work (LAB2), 3,5 credits, marks Fail (U), 3, 4 or 5
Written and/or oral examination (TEN1), 1,5 credits, marks Fail (U), 3, 4 or 5

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail