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Uppsala University
Department of Information Technology
Scientific
Computing |
Finite Element Methods
2012-10-30 |
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.
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