Course syllabus

Course-PM for VSM167

VSM167 Finite element method - basics lp2 HT23 (7.5 hp), offered by the Department of Industrial and Materials Science.

This course homepage will be the main channel of information, containing all the material, notifications and updates, the current schedule, answers to questions and other important information. Please check out the homepage on a daily basis and/or sign up for daily notifications from Canvas, e.g. to be aware of schedule changes

Contact details

Lecturers and examiner:
Martin Fagerström (MF),, ph. 070-2248731
Jim Brouzoulis (JB), (examiner MHA021)

Teaching assistants:
Mohammad Salahi Nezhad,
Luis Gulfo,
Rauan Al-Emrani,
Victor Mathiesen,

Course aim

The aim of the course is to provide the theoretical foundation and understanding of the finite element method (FEM), which is the predominant numerical method used for analysis and design in the structural, mechanical, rock, energy and environmental engineering areas. The course gives the necessary prerequisites for the course Finite Element Method – Structures (TME245).


A detailed schedule is available in the course memo as well as on TimeEdit.

Course literature

An additional list of reference literature is given below. These texts are recommended for those who want to broaden their knowledge.

  • Zienkiewicz and R.L. Taylor. The finite element method, Vol. 1-3, 7th ed. Butterworth-Heineman, 2013
  • K-J. Bathe. Finite element procedures. Prentice-Hall, 1996
  • Cook, D.S. Malkus and M.E. Plesha. Concepts and applications of finite element analysis. John Wiley & Sons, 1989.
  • R. Hughes. The finite element method. Linear static and dynamic finite element analysis. Prentice-Hall, 1987.

Course design

The course content is defined by this course memo. Some lecture material will be prepared in advance and will be available for downloading from the course homepage (Canvas). Frequent references will be made in class to the textbook by Ottosen and Petersson, see Literature list below. However, it must be noted that deviations from this book in presenting the material as well as the used notation can occur.

The course is organised into lectures, a few tutorials and computer classes. The main theory is presented during the lectures. The theory is then exemplified during the tutorials and utilised to solve the graded projects during the computer classes.

The projects are to be solved in groups of preferably two students. More than two students will not be allowed and since we believe that you will learn more by workingin pair, two students per group is the strong recommendation.  The main intention with these projects is to give all the students the opportunity to really work with the theory and to apply the theory to solve “real” FE problems. The best way to study the finite element method is “learning-by-doing”! So make sure to take an active part in solving the tasks.

The projects are also a key part of the course examination, cf. below. Consequently, finalising these projects with good grades will require considerable effort, and more time than what is set aside for the supervised computer classes will in general be required. Submission of project reports after the deadlines will not be considered unless agreed upon beforehand.

Changes made since the last occasion

This ýear we change from using Comsol Multiphysics to using Abaqus as the commercial finite element software to be used for solving some of the hand-in assignments.

Learning objectives and syllabus

After completion of this course, the student should be able to:

  • Define the basic constituents defining a boundary value problem, in terms of a differential equation, data and boundary conditions, e.g. equilibrium for a structure with loads and supports.
  • Identify and separate the physical modeling (balance laws, material properties, loads and boundary conditions) as compared to the discretization (numerical solution, e.g. FEM).
  • From the boundary value problem on strong form (the partial differential equation and boundary conditions),-derive the corresponding weak formulation for heat flow and elasticity problems.
  • From the weak form, derive the corresponding finite element form.
  • Derive the weak and finite element form of transient problems (applied to heat flow problems).
  • Apply the basic theory of the finite element method as a numerical method to solve (partial) differential equations, involving the derivation of element contributions (element stiffness matrix and load vector) and the construction of suitable approximating functions (incluing isoparametric element formulation and numerical integration),-
  • Apply the finite element method to problems of stationary and transient heat flow and linear static elasticity in one, two and three spatial dimensions.--
  • Formulate the finite element method as a computational algorithm and implement simple finite element programs in MATLAB for one and two dimensional problems.
  • Judge and assess simulation results, and based on these results draw conclusions of whether the design meet the relevant design criteria or not.
  • Analyse the robustness and reliability of the simulation results with respect to uncertainty in input data, and to reflect on the validity of conclusions drawn from these results.

Examination form

The examination is a combination of hand-in project and a final written exam (for final grading see below):


The main course work consists of one mandatory and two semi-mandatory projects. The computer projects involve FE-analysis using the Matlab toolbox CALFEM as well as the commercial FE-software COMSOL. The CALFEM package can be downloaded from the course homepage or from

The projects are to be solved in groups of maximum two students where both students should contribute equally in solving the tasks. Computer classes are scheduled where you will have access to teaching assistants for asking questions about the projects. Please note however, that we will not answer direct questions like “Is this correct?”. It is up to each individual group to make sure that the answers are reasonable.

A written report for each project must be submitted via Canvas by the deadline (see course schedule). Besides addressing all the subtasks, the report should include a short statement of how of which group member did what should be included in each report. Reports may be handwritten, but in such cases extra care should be taken so that reports are readable and understandable. In order to be able to submit the report, you need to sign-up for one of the project groups.

It is mandatory to fully complete the first project, which means that students will be required to update their reports until everything is correct. This must be done before the exam and will then render 4 credit points. For projects 2 and 3, a maximum of 4 credits can be obtained. Altogether, 12 credit points can thus be obtained towards the final grade, see below. These points will remain valid until the course is given next time. Please note that project reports will be graded without any possibility for modifications or improvements in a second stage.

Since the projects are a significant part of the examination, it is essential that each group solves the tasks separately. To clarify better, it is OK to:

  • collaborate and discuss around derivations asked for in different subtasks. HOWEVER, each group should in the end do the derivations themselves and hand-in their own written solutions
  • discuss around implementation strategies in MATLAB for different subtasks. HOWEVER, limit the discussions to pen and paper discussions otherwise you will know that you are on the border of what is not OK.

It is NOT OK to:

  • Directly copy other groups derivations and hand them in as your own. This applies also to codes from students from previous years.
  • Show or share any amount of MATLAB-code or COMSOL files between groups. 
  • Copy and hand-in code which is partly written by another group. This is true for code written by other students this year as well as from previous years.

Project reports will be analysed trough Urkund. Any suspected cheating (including things like copying MATLAB code or parts of someone else’s report) will be directly reported to the Disciplinary Committee, please refer to the collection of rules:

Please note that failure to comply with the rules may lead to warnings or in worst case time limited suspension form Chalmers.

Regarding the ambition level and quality of the project reports, imagine the current situation: The person correcting and grading the report is your manager at the consultancy company where you work. You have been given an FE assignment and when you hand in the results your manager should be able to send the report directly to the client without further modification.

Final exam

The final written exam takes place in a computer room in the morning on Thursday, 11 January at 8:30. During the exam, you will have access to MATLAB and CALFEM, which are tools that will be used throughout the course. Short programming tasks may therefore be part of the exam. The only additional aids that will be allowed are a Chalmers type approved pocket calculator and a formula sheet that will be appended to the exam. The exam will have questions/problems which altogether can give 18 credit points.


The final course grade is given as a combination of the credit points obtained at the exam and from the projects according to the table below:

Grades are awarded as follows:

Required credit points

Chalmers grade



15 (minimum 6 from the final exam)






 NOTE: To obtain a passing grade it is necessary to obtain at least 6 points in the final exam as well as completion of at least one computer assignment.

Course summary:

Date Details Due