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Instructor:
Malgorzata Peszynska
Class:
MWF 9:00-9:50, STAG 107,
CRN: 14467 (
MTH 654 ) or 14469 (
MTH 659 )
Course information:
The Finite Element Method (FEM) is a numerical method for solving
partial differential equations. It provides foundation for most
contemporary methods of analysis and discretization applied to
engineering design, computational fluid dynamics, and mass and energy
flow and transport. Please read Course
Announcement for more background.
Syllabus:
In the course we will develop the mathematical foundations and
algorithmic aspects of FEM. Topics will include error estimates,
stability analysis, grid adaptivity, and implementation issues. We
will focus on linear stationary problems but, time permitting,
nonlinear and nonstationary problems will be also discussed. The
necessary mathematical background in functional analysis, numerical
integration, interpolation and approximation theory will be
developed. The assignments will be a mixture of theoretical and
computational exercises. For implementation, templates will be
provided both in MATLAB and via public-domain libraries, and a
computer lab will be held to help students develop their projects.
Students:
The course is intended for graduate students of mathematics and
various science and engineering disciplines. The basics of real
variables and differential equations are required. Familiarity
with numerical methods, partial differential equations, and familiarity
with computer programming are a plus but are not required.
The assignments will be a mixture of theoretical and computational
exercises. Please contact the instructor with questions.
Course Outcomes: A successful student will be able to
- Set-up variational setting of elliptic BVPs in Hilbert spaces
and their Finite Element approximation
- Use a variety of Finite Element spaces and determine an
appropriate order of convergence theoretically and numerically
- Carry out an implementation and convergence tests of
finite element algorithms using provided templates
Special arrangements for students with disabilities,
make-up exams etc.: please contact the instructor and Services for Students with
Disabilities, if relevant, and provide appropriate
documentation.
Course drop/add information is at
http://oregonstate.edu/registrar/.
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