 Department of Information Technology TDB Courses Finite Element Methods Schedule Assignments Laborations Examination
 Uppsala University Department of Information Technology Scientific Computing Finite Element Methods2012-10-30

Finite Element Methods

(http://www.it.uu.se/edu/course/homepage/fem/ht12)

Teacher
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
English.

Program
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.

Literature
• 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.