Topic outline

  • Lectures

    On weeks marked as Lectures, a new section of lecture notes and a set of lecture videos will be published. Students should study the provided material independently, do the given assignments (mostly) on pen and paper and return the exercises via MyCourses.
     - Questions can be asked via Zulip.
     - Cooperation between students for exercises is allowed and even encouraged. However, your own thinking and understanding should be visible in your solutions. For example, you may sketch the exercises with other students on e.g. a white board, and then write a cleaned solution individually to be returned via MyCourses.

    Computer exercises

    On weeks marked as Computer exercises, during the scheduled lecture hours, computer exercises are remotely run. A set of Matlab exercises is published to be returned via MyCourses. The exercises can be started during the "lecture hours" and finished afterwards.
    It is strongly recommended to do these problems in a group of 2-3 people!
     - We will provide a Zoom "breakout room" for each group and provide assistance during the lecture hours.
     - You can communicate via Zoom, gather together in a location chosen by you or use whatever other means of communication you prefer. However, the support during the lecture hours is provided via Zoom. Please ensure you can share your code (and/or screen) during lecture hours in case you need help.
     - Later, further questions can be asked via Zulip.
     - However, everyone should return their own code.

    Project work

    The last 4-5 weeks of this course consist of a project work involving an application or an extension of FEM. The project is carried out preferably in groups of 2-3 people. You will produce a short (~10-15 minute) presentation which is presented during lecture hours on Week 12 via Zoom.



    Week 1 / 11.1.2021 / Lectures:

    - 1D Finite element method
    - Classical (strong) partial differential equation (PDE) to weak form
    - Finite element analysis workflow
    - Finite element solution process

    Week 2 / 18.1.2021 / Computer exercises:

    - Extensions of 1D FEM
    - Second order basis
    - Different PDEs (non-constant coefficients + lower order term)
    - Computing linear functionals of the solution
    - Empirical error analysis

    Week 3 / 25.1.2021 / Lectures:

    - Briefly on PDE theory: existence of solution to 1D Poisson equation
    - Sobolev spaces H¹ and H²
    - Poincare's inequality
    - Weak derivative

    Week 4 / 1.2.2021 / Lectures:

    - FEM in 2D
    - Affine mapping concept
    - Change of variables formula
    - Integration over triangle

    Week 5 / 8.2.2021 / Computer exercises:

    - Programming 2D FEM solver

    Week 6 / 15.2.2021 / Lectures:

    - FEM error analysis theory

    Exam week / 22.2.2021

    - No teaching

    Week 7 / 1.3.2021 / Computer exercises:

    - Empirical error analysis for 2D FEM
    - Effect of domain, load and mesh density to error

    Week 8 / 8.3.2021 / Lectures, project work:

    - Overflow/project topic presentations.
    - Project meetings with groups.

    Weeks 9-11 / 15.3.2021 / Project work:

    - Independent work on projects. Support from Antti and Topi via Zoom/Zulip

    Week 12 / 5.4.2021 / Project presentations:

    - Project presentations via Zoom.

    Week 13 / 12.4.2021 / Exam week:

    - Course exam, published on 13.4.2021 at 08:00, to be returned by 23:59.
    - Exam, similar to course exam except brutally difficult.