MTH 655
and
MTH 659 (Numerical Analysis)
Numerical Functional Analysis with Applications
- Winter 2011
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INSTRUCTOR:
Malgorzata Peszynska
CLASS:
MWF 11:00-11:50, CRN: 36197 (MTH 655)/ 37728 (MTH 659)
COURSE INFORMATION:
Do you have interest in foundations of numerical analysis such as
interpolation and approximation theory ? Do you want to learn how to
solve numerically differential equations with singularities and/or on
irregular domains and/or want to go beyond finite differences ? Or,
you already know classical finite elements for second order elliptic
problems, but want to know more ? Or perhaps need to estimate
numerical errors or deal with uncertain data ?
This class will cover a variety of applications of numerical
functional analysis and in particular selected topics from the Finite
Element (FE) method. The course is intended for graduate students of
mathematics and various science and engineering disciplines who have
some course or project experience with numerical analysis/scientific
computing, or those who want to explore selected applied functional
analysis topics in the numerical setting.
We will first give a compact introduction/review of Galerkin FE method
for approximation of variational solutions to boundary value
problems. Next, we will discuss i) mixed and hybrid FE, error
estimates and estimators in various norms and quantities of interest,
ii) develop methods suitable in optimization, eigenvalue problems, and
integral equations, and iii) lead an excursion into stochastic FE and
iv) motivate the underlying physical models from fluid and solid
mechanics. The class will provide mathematical details; the templates
of the algorithms used in exercises will be made available to the
students. The assignments will be a mixture of analysis and
computations.
STUDENTS:
This breadth of topics will require not much more than solid real
variables, differential equations, and linear algebra background, plus
basic computing skills; the stochastic part will require familiarity
with probability concepts. Questions concerning pre-requisites should be
addressed to the instructor.
TEXTBOOK: most topics are covered in Atkinson/Han ``Theoretical
Numerical Analysis, A Functional Analysis Framework'' (Springer,
2000).
(This book is listed by OSU library as
a
Springer online resource .)
You can supplement the FE material with one of several excellent
textbooks on FE including those by Braess, Bangerth/Rannacher,
Becker/Carey/Oden, Brenner/Scott, Ciarlet, Johnson, and many
others. [If you have one already, you do not need a new one, but if
you have none, I can suggest one based on your background].
SEQUENCE MTH 654-656 in 2010-2011:
This course is the second in a
year-long sequence, and the courses in this sequence can be taken
independently.
GRADING: will reflect the student's learning derivative shown
in the solutions to the assigned projects.
Course drop/add information is at
http://oregonstate.edu/registrar/.
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