Thursday, Sep. 4, 9:30 am in MTH 3206, University of Maryland,
College Park
The n-width of the solution space of a 2 dimensional
singular perturbation problem
Prof. R. Bruce Kellogg
Department of Mathematics,
University of Maryland,
College Park
The solutions of singular perturbation problems
display boundary layers and other transition regions.
These boundary layers affect the approximability of the
solutions, and therefore the accuracy of finite element methods
for these problems. The Kolmogorov n-width is a concept
that enables one to measure the approximability of a set of
functions. In this talk, which represents some
work with Martin Stynes,
precise estimates will be given for the n-width of the
set of solutions to a self-adjoint singular perturbation problem
in two dimensions. This n-width provides an upper bound to
the accuracy of a finite element solution if the data is in
a certain regularity class.
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