Uppsala universitet
Department of Information Technology

TDB Courses

Finite Element Methods





Uppsala University
Department of Information Technology
Scientific Computing
Finite Element Methods

Finite Element Methods


Exam 10-12-21
Suggested solutions

Exam 11-04-26
Suggested solutions

Stefan Engblom
Room: 2422
Phone: 018-4712754
E-mail: stefan.engblom@it.uu.se

Latest news
  • Formulas, inequalities or equations you definitely should know include: Cauchy-Schwartz and Poincaré inequalities (the latter with the simple 1D proof, see Ex 2.7 in MGL), Euler forward/backward, Trapezoidal/Crank-Nicolson rule, Green's formula, quadratures: trapezoidal+midpoint rules.
  • Will be provided at the exam (if necessary): trace inequalities and interpolation estimates. Mathematics handbook for science and engineering may be used.

  • Given a general linear ODE on the form My' = -Ay, the generalized eigenvalue decomposition is a way to diagonalize it. The result is a set of decoupled scalar ODEs (with the scalars being in fact minus the eigenvalues of A). [A very quick derivation now runs as follows: given My' = -Ay, where M = L*L' (from Cholesky factorization), L'y' = -L'AL*L'y, or with z := L'y and B := L'AL, z' = -Bz = -UDU'z (from eigendecomposition of B), or with w := U'z, w' = -Dw. D is a diagonal matrix with the eigenvalues of B (or A, they are the same) on the diagonal.]
  • Some comments on the gain in doing the assignments added under Assignments and Examination.
  • Two more exams (from 2010) added under Examination.
  • Suggested extra material: FEM lectures by Gilbert Strang, FEM 1D part 1, FEM 1D part 2.
  • There are suggested solutions to most exercises. You find them under Schedule (follow the links under 'Topics').
  • IMPORTANT: If you register for the course but decides to discontinue taking it, be sure to report this fact to the Student Office it-kansli@it.uu.se. The registration can be removed if you do this within 3 weeks from start.
  • 2010-10-26 The first lecture is in P2446 at 1515.

  • Course PM
    Is available here.

    Language of Instruction

    The course consists of 12 lectures, 6 exercise classes, and 3 laborations. Two lectures are given by external visitors and are important to the learning objectives of the course. These two lectures are therefore mandatory. The laborations count as 2.0 hp, while the written exam makes up for the remaining 3.0 hp. There are three voluntarily assignments: if you submit them before deadline I will correct them and give feedback.

    1. (MGL) Larson, M.G., Bengzon, F.: The Finite Element Method: Theory, Implementation, and Practice. Department of Mathematics, Umeå University 2009.
    2. Johnson, C.: Numerical Solution of Partial Differential Equations by the Finite Element Method. Studentlitteratur, 1987.
    3. Eriksson, K., Estep, D., Hansbo, P. & Johnson, C. : Computational Differential Equations. Studentlitteratur, 1997.
    We will follow reference 1 closely. It is available for free.