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Applied Finite Element Methods, 5.0 c

Course code:1TD056, Report code:12006, 33%, DAG, NML
week: 45 - 03 Semester: Autumn 2019 (2019-11-04 - 2020-01-19)

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Registration is open: 2019-10-07 - 2019-11-10

Information for admitted students

Please find our information at the Bulletin board:
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Contact information

If you have any questions about registration, please contact:
Name: IT-kansliet / Student Office
Email: it-kansli@it.uu.se
Telephone: 018-4717604

Information about student accounts

To take this course you must have a student account. As an admitted you can activate your student account via www.uu.se/konto.

Course information

Course description

The main focus is on solutions to partial differential equations and methods for solving the resulting equation system. Solution methods based on finite differences and finite element methods. Direct (based on LU-factorization) and iterative methods for solutions to linear systems of equations. Theoretical, practical, implementational, as well as validation aspects, are discussed in relation to the methods presented in the course. Use of computational software (MATLAB). Examples of key concepts covered in the course: accuracy and order of accuracy, efficiency, consistency, stability, convergence.


Lecturer: Murtazo Nazarov
Office: ITC building 2, floor 4, room 2421
Email: murtazo.nazarov”AT”it”DOT”uu”DOT”se
Office hours: Fridays 13:15-14:00, or by appointments

Teaching plan

There will be 12 lectures, 2 midterm exams, 3 exercise sessions, and 3 labs.


120 credits in science/engineering including 30 credits in mathematics, where linear algebra and vector calculus must be covered. Scientific Computing III.

Course literature

Larson, M.G., Bengzon, F., The Finite Element Method: Theory, Implementation, and Practice. Department of Mathematics, Umea University 2009.

K. Eriksson, D. Estep, P. Hansbo, C. Johnson. Computational Differential Equations. Studentlitteratur, ISBN ISBN 91-44-49311-8.

C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method.

Alexandre Ern, Jean-Luc Guermond. Theory and Practice of Finite Elements. ISBN 978-0-387-20574-8.


There will three laboratory sections. The labs help you in solving the project, but they are not graded. Description of the labs and the project is available in the student portal.

  • Lab 1: Finite element method in 1D
  • Lab 2: Finite element method in 2D
  • Lab 3: The FEniCS project

Programming assignments

There will be one mandatory programming project which consists of three parts. The project must be done indivudially: you will submit your code and write a report. Follow the instruction below about writing your report. The report should be submitted through the student portal, where all works are checked for plagiarism. There will be three deadlines for each three-part of the project. Always submit your work before the deadline, if you miss the deadline without any reason (especially if you miss the last deadline) you will have to wait until the next course or re-examination period.


  • Part A:
  • Part B:
  • Part C:

Guidelines for writing the final report

Note: for Part A and Part B, you need to submit a minimal report such that it is clear that you solved the task. For example, for each problem write your solution, include figures, put proper information in the figures, include your code at the bottom of the file. Then, together with Part C, you will have to write a complete report that includes all parts in more detail.

Do not submit many output files, Matlab files, etc. Submit only one (!) pdf file for each part.

Your final report may look like as follows:

  • The first page of the report should state clearly:
    • Name (and email address) of the student
    • Title
    • Date of Submission
  • A typical report structure could look something like That is just one possibility, there are many others! Given the scope of the project.
    • Introduction
    • Part A
    • A short introduction to Part A, for example, what are the aim and goals, etc.
    • Problem 1: some theory and results
    • Problem 2: ...
    • Part B
    • A short introduction to Part B
    • Problem 1: some theory and results
    • Problem 2: ...
    • ...
    • Concluding discussion
    • Attached code
  • For each solution, you should provide the required theory, (when appropriate) implementation details. The figures and tables must be self informative. They should have a proper title, labels, and clearly visible. Make an effort in discussing and reflecting upon the results. The code should be attached by the end of the report. Since the code is an essential part, it should be as readable as the report.
  • It is expected that you discuss your work before it is submitted, but copying is cheating and is unacceptable.

Exercise sessions

During the exercise sessions, we will solve a set of problems corresponding to each block of the book, as well as some old examinations. Attending the exercise sessions helps you to understand materials covered at the lectures and prepares you for the final exam.


The course is graded with respect to your final examination and your project achievement. The course is completed only if you pass all your programming assignments and the exam. 
Project: 2 points
Final: 3 points

Weekly plan


Scholastic Dishonesty

Students may work together and discuss the homework problems with each other. Copying work done by others is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. For more information on university policies regarding scholastic dishonesty, see the University of Uppsala’s policy at http://www.it.uu.se/edu/fusk.

Students with Disabilities

According to the University regulation, all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you need help or want to get more information about it please contact the University of Uppsala’s services for students with disabilities.