SF2561 The Finite Element Method 7.5 credits

Finita elementmetoden

A second course on computational methods focusing on the finite element method (FEM) and partial differential equations.

  • Education cycle

    Second cycle
  • Academic level (A-D)

  • Main field of study

    Mathematics
    Technology
  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 18 SAP for Study Abroad Programme (SAP)

  • Periods

    Autumn 18 P1 (7.5 credits)

  • Application code

    10021

  • Start date

    27/08/2018

  • End date

    2018 week: 43

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Number of lectures

  • Number of exercises

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Planned timeslots

    P1: E1, F1, F2. more info

  • Course responsible

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Teacher

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Target group

    Only for SAP-students. Students from UCAS.

Autumn 18 for programme students

Autumn 17 for programme students

Autumn 17 for Study Abroad Programme (SAP)

  • Periods

    Autumn 17 P1 (7.5 credits)

  • Application code

    10077

  • Start date

    28/08/2017

  • End date

    2017 week: 43

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Number of lectures

  • Number of exercises

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Course responsible

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Teacher

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Target group

    Study Abroad Programme

Intended learning outcomes

Basic laws of nature are typically expressed in the form of partial differential equations (PDE), such as Navier’s equations of elasticity, Maxwell’s equations of electromagnetics,Navier-Stokes equations of fluid flow, and Schrödinger’s equations of quantum mechanics. The Finite element method (FEM) has emerged as a universal tool for the computational solution of PDEs with a multitude of applications in engineering and science. Adaptivity is an important computational technology where the FEM algorithm is automatically tailored to compute a user specified output of interest to a chosen accuracy, to a minimal computational cost.

This FEM course aims to provide the student both with theoretical and practical skills, including the ability to formulate and implement adaptive FEM algorithms for an important family of PDEs.

The theoretical part of this course deals mainly with scalar linear PDE, after which the student will be able to

  • derive the weak formulation
  • formulate a corresponding FEM approximation;
  • estimate the stability of a given linear PDE and it’s FEM approximation;
  • derive a priori and a posteriori error estimates in the energy norm, the L2-norm,
    and linear functionals of the solution;
  • state and use the Lax-Milgram theorem for a given variational problem.

Having completed the practical part of the course the student will be able to:
modify an existing FEM program to solve a new scalar PDE (possibly nonlinear);

  • implement an adaptive mesh refinement algorithm, based on an a posteriori error
  • estimate derived in the theoretical part;
  • describe standard components in FEM algorithms.

Course main content

  • FEM-formulation of linear and non-linear partial differential equations, element
    types and their implementation, grid generation, adaption and error control, efficient
    solution algorithms (e.g. by a multigrid method).
  • Applications to stationary and transient diffusion processes, elasticity, convectiondiffusion,
    Navier-Stokes equation, quantum mechanics etc

Eligibility

Single course students: 90 university credits including 45 university credits in Mathematics
or Information Technology. English B, or equivalent.

Recommended prerequisites

DN2221 Applied Numerical Methods, part 1 (or corresponding), can be read in parallel.

Literature

To be announced at least 4 weeks before course start at course web page. Previous year:
K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations.
Studentlitteratur, ISBN 91-44-49311-8

Examination

  • LAB2 - Laboratory Work, 4.5, grading scale: P, F
  • TEN2 - Written Examination, 3.0, grading scale: A, B, C, D, E, FX, F
  • LAB2 - Laboratory Task, 4.5 credits, grade scale: P, F
  • TEN2 - Examination, 3.0 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

  • Examination (TEN2; 3 university credits).
  • Assignments (LAB2; 4.5 university credits).

Offered by

SCI/Mathematics

Contact

Sara Zahedi (sara.zahedi@math.kth.se)

Examiner

Sara Zahedi <sara.zahedi@math.kth.se>

Add-on studies

Please discuss with the course leader.

Version

Course syllabus valid from: Autumn 2013.
Examination information valid from: Autumn 2013.