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Spring 2006 -- 642:575

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NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

INSTRUCTOR:

Richard S. Falk

Hill 722

445-2367

email: falk@math.rutgers.edu

Course Web Page

In this course, we study finite difference, finite element, and finite volume
methods for the numerical solution of elliptic, parabolic, and hyperbolic
partial differential equations. The course will concentrate on the key ideas
underlying the derivation of numerical schemes and a study of their stability
and accuracy. Students will have the opportunity to gain computational
experience with numerical methods with a minimal of programming by the use of
* Matlab's PDE Toolbox* software.

Since there are many sophisticated computer packages available for solving
partial differential equations, one might think that a thorough understanding
of the numerical methods employed is no longer necessary. A striking example
of why naive use of such codes can lead to disastrous results is the sinking
of the Sleipner A offshore oil platform in Norway in 1991, resulting in an
economic loss of about $700 million. The post accident investigation traced
the problem to inaccurate finite element approximation of the linear elastic
model of the structure (using the popular finite element program NASTRAN). The
shear stresses were underestimated by 47%, leading to insufficient design.
More careful finite element analysis, made after the accident, predicted that
failure would occur with this design at a depth of 62m, which matches well
with the actual occurrence at 65m.

For more information on this disaster, see the web site:
Disaster