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Convergence rates of AFEM with <i>H <sup>-1</sup></i> Data

Friday, December 3, 2010 - 2:45pm - 3:30pm
Keller 3-180
Ricardo Nochetto (University of Maryland)
In contrast to most of the existing theory of adaptive
finite
element methods (AFEM), we design an AFEM for -Δ u =
f
with right hand side f in H -1 instead of
L2. This
has
two important consequences. First we formulate our AFEM in
the
natural space for f, which is nonlocal. Second, we show
that
decay rates for the data estimator are dominated by those
for the
solution u in the energy norm. This allows us to conclude
that
the performance of AFEM is solely dictated by the
approximation
class of u.

This is joint work with A. Cohen and R.
DeVore.
MSC Code: 
65N30
Keywords: