Title:  Convergence of adaptive finite element methods for controlling
local energy errors

Abstract:  Adaptive finite element methods (AFEM) for elliptic
problems have long been used in practice, but it is only in recent
years that their convergence and optimality properties have been
studied extensively from a theoretical perspective.   Most studies on
AFEM convergence assume that the norm being controlled is the global
energy norm, but in practice it is often desirable to instead control
other error norms or functionals.  We define an AFEM for controlling
local energy norms and prove several different convergence results.
We will also briefly discuss recent joint work with R. Stevenson in
which we establish convergence and optimality of an AFEM for
controlling $L_2$ errors.