
Uppsala University
Department of Information Technology Scientific
Computing 
Finite Element Methods 20121030 
Finite Element Methods
(http://www.it.uu.se/edu/course/homepage/fem/ht12)
Teacher
Stefan Engblom
Room: 2422
Phone: 0184712754
Email: stefan.engblom@it.uu.se
Latest news
Formulas, inequalities or equations you definitely should
know include: CauchySchwartz and Poincaré inequalities (the latter
with the simple 1D proof, see Ex 2.7 in MGL), Euler forward/backward,
Trapezoidal/CrankNicolson 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.]
Inclass
exercise: Selfassessment test
#2.
Outofclass
exercise: Selfassessment test
#1.
Inclass 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 itkansli@it.uu.se. The
registration can be removed if you do this within 3 weeks from start.
20121030 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.
