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The conventional strategy for controlling the error in finite-element
methods is based on a posteriori estimates for the error
in the global "energy" or L_{2}-norm involving
local residuals of the computed solution. Such estimates contain
constants describing the local approximation properties of the
finite-element space and the stability properties of a linearized
dual problem. The mesh refinement then aims at equilibrating
the local error indicators. However, meshes generated in this
way via controlling the error in a global norm may not be appropriate
for local error quantities like point values or contour integrals,
and in the case of strongly varying coefficients. This deficiency
may be overcome by introducing weight factors in the a posteriori
error estimates which depend on the dual solution and contain
information about the relevant error propagation. In this way
optimal economical meshes can be obtained for various kinds
of error measures. This will be illustrated for simple model
cases as well as for a nonlinear problem in perfect plasticity.
Another application is the computation of local quantities in
viscous flows as, for example, drag and lift of a blunt body,
which will be discussed in the talk by Roland Becker.
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