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


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' = -inv(L)*A*inv(L')*L'y, or with z := L'y and B := inv(L)*A*inv(L'), 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.]
  • In-class exercise: Self-assessment test #2.
  • Out-of-class exercise: Self-assessment test #1.
  • In-class exercise: Sort it out!.
  • Suggested extra material: FEM lectures by Gilbert Strang, FEM 1D part 1, FEM 1D part 2.
  • 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.
  • 2012-10-30 The first lecture is in P2245 at 1315. Welcome!

  • Course PM
    Is available here.

    Language of Instruction

    The course consists of 12 lectures, 6 exercise classes, and 3 laborations. The three mandatory assignments count as 2.0 hp, while the written exam makes up for the remaining 3.0 hp.

  • Larson, M.G., Bengzon, F.: The Finite Element Method: Theory, Implementation, and Practice. Department of Mathematics, Umeå University 2009. ("MGL")
  • Johnson, C.: Numerical Solution of Partial Differential Equations by the Finite Element Method. The 2009 edition can be downloaded from here. Note: link not tested.

  • We will follow MGL closely. It is available for free.